hamiltonian perspective on compartmental reaction diffusion networks inspired by the recent developments in modeling and analysis of reaction networks we provide a geometric formulation of the reversible reaction networks under the influence of diffusion using the graph knowledge of the underlying reaction network the obtained reaction diffusion system is a distributed parameter port hamiltonian system on a compact spatial domain motivated by the need for computer based design we offer a spatially consistent discretization of the pde system and in a systematic manner recover a compartmental ode model on a simplicial triangulation of the spatial domain exploring the properties of a balanced weighted laplacian matrix of the reaction network and the laplacian of the simplicial complex we characterize the space of equilibrium points and provide a simple stability analysis on the state space modulo the space of equilibrium points the paper rules out the possibility of the persistence of spatial patterns for the compartmental balanced reaction diffusion networks

direct frequency domain deconvolution when the signals have no spectral inverse a method for frequency domain deconvolution when the kernel has no spectral inverse is presented discrete frequency interpolation is used to avoid zero valued frequency samples the algorithm does not suffer from the spectral singularities of the original kernal and its complexity is proportional to that of the fast fourier transform a comparative noise study showed improved performance relative to the direct frequency domain method

discrete time port hamiltonian systems a definition based on symplectic integration abstract we introduce a new definition of discrete time port hamiltonian ph systems which results from structure preserving discretization of explicit ph systems in time we discretize the underlying continuous time dirac structure with the collocation method and add discrete time dynamics by the use of symplectic numerical integration schemes the conservation of a structural discrete time energy balance expressed in terms of the discrete time dirac structure extends the notion of symplecticity of geometric integration schemes to open systems we discuss the energy approximation errors in the context of the presented definition and show that their order for linear ph systems is consistent with the order of the numerical integration scheme implicit gauss legendre methods and lobatto iiia iiib pairs for partitioned systems are examples for integration schemes that are covered by our definition the statements on the numerical energy errors are illustrated by elementary numerical experiments

high order geometric methods with exact conservation properties conservation laws in for example electromagnetism solid and fluid mechanics allow an exact discrete representation in terms of line surface and volume integrals in this paper we develop high order interpolants from any basis that constitutes a partition of unity which satisfy these integral relations exactly the resulting gradient curl and divergence conforming spaces have the property that the conservation laws become completely independent of the basis functions hence they are exactly satisfied at the coarsest level of discretization and on arbitrarily curved meshes as an illustration we apply our approach to b splines and compute a 2d stokes flow inside a lid driven cavity which displays amongst others a point wise divergence free velocity field

the frequency decomposition multi grid method a new variant of the multi grid algorithms is presented it uses multiple coarse grid corrections with particularly associated prolongations and restrictions in this paper the robustness with respect to anisotropic problems is considered

interconnection and damping assignment passivity based control of port controlled hamiltonian systems passivity based control pbc is a well established technique that has shown to be very powerful to design robust controllers for physical systems described by euler lagrange el equations of motion for regulation problems of mechanical systems which can be stabilized shaping only the potential energy pbc preserves the el structure and furthermore assigns a closed loop energy function equal to the difference between the energy of the system and the energy supplied by the controller thus we say that stabilization is achieved via energy balancing unfortunately these nice properties of el pbc are lost when used in other applications which require shaping of the total energy for instance in electrical or electromechanical systems or even some underactuated mechanical devices our main objective in this paper is to develop a new pbc theory which extends to a broader class of systems the aforementioned energy balancing stabilization mechanism and the structure invariance towards this end we depart from the el description of the systems and consider instead port controlled hamiltonian models which result from the network modelling of energy conserving lumped parameter physical systems with independent storage elements and strictly contain the class of el models

explicit simplicial discretization of distributed parameter port hamiltonian systems simplicial dirac structures as finite analogues of the canonical stokes dirac structure capturing the topological laws of the system are defined on simplicial manifolds in terms of primal and dual cochains related by the coboundary operators these finite dimensional dirac structures offer a framework for the formulation of standard input output finite dimensional port hamiltonian systems that emulate the behavior of distributed parameter port hamiltonian systems this paper elaborates on the matrix representations of simplicial dirac structures and the resulting port hamiltonian systems on simplicial manifolds employing these representations we consider the existence of structural invariants and demonstrate how they pertain to the energy shaping of port hamiltonian systems on simplicial manifolds

stable three point wavelet bases on general meshes recently we introduced a wavelet basis on general possibly locally refined linear finite element spaces each wavelet is a linear combination of three nodal basis functions independently of the number of space dimensions in the present paper we show h s stability of this basis for a range of s that in any case includes s 1 which means that the corresponding additive schwarz preconditioner is optimal for second order problems furthermore we generalize the construction of the wavelet basis to manifolds we show that the wavelets have at least one and in areas where the manifold is smooth and the mesh is uniform even two vanishing moments because of these vanishing moments apart from preconditioning the basis can be used for compression purposes for a class of integral equation problems the stiffness matrix with respect to the wavelet basis will be close to a sparse one in the sense that a priori it can be compressed to a sparse matrix without the order of convergence being reduced

on the synthesis of boundary control laws for distributed port hamiltonian systems this paper is concerned with the energy shaping of 1 d linear boundary controlled port hamiltonian systems the energy casimir method is first proposed to deal with power preserving systems it is shown how to use finite dimensional dynamic boundary controllers and closed loop structural invariants to partially shape the closed loop energy function and how such controller finally reduces to a state feedback when dissipative port hamiltonian systems are considered the casimir functions do not exist anymore dissipation obstacle and the immersion via a dynamic controller reduction through invariants method cannot be applied the main contribution of this paper is to show how to use the same ideas and state functions to shape the closed loop energy function of dissipative systems through direct state feedback i e without relying on a dynamic controller and a reduction step in both cases the existence of solution and the asymptotic stability by additional damping injection of the closed loop system are proven the general theory and achievable closed loop performances are illustrated with the help of a concluding example the boundary stabilization of a longitudinal beam vibrations

estimating the order of a fir filter for noise cancellation the problem of designing a finite impulse response filter devoted to the joint process problem and in particular to noise cancellation is investigated the goal is restricted to how to choose an optimal order of the fir filter the analysis is based on the maximization of a noise reduction criterion which is in fact perfectly matched to the desired performance namely the minimization of residuals the criterion includes estimation errors introduced by the substitution of the true covariance matrices for estimates since true covariance matrices again enter the noise reduction criterion they must be replaced by estimates the criterion is then modified in order to take this fact into account but the scheme is not iterated any further simulations are presented for various simple cases

a generalized framework for nodal first derivative summation by parts operators a generalized framework is presented that extends the classical theory of finite difference summation by parts sbp operators to include a wide range of operators where the main extensions are i non repeating interior point operators ii nonuniform nodal distribution in the computational domain iii operators that do not include one or both boundary nodes necessary and sufficient conditions are proven for the existence of nodal approximations to the first derivative with the sbp property it is proven that the positive definite norm matrix of each sbp operator must be associated with a quadrature rule moreover given a quadrature rule there exists a corresponding sbp operator where for diagonal norm sbp operators the weights of the quadrature rule must be positive the generalized framework gives a straightforward means of posing many known approximations to the first derivative as sbp operators several are surveyed such as discontinuous galerkin discretizations based on the legendre gauss quadrature points and shown to be sbp operators moreover the new framework provides a method for constructing sbp operators by starting from quadrature rules this is illustrated by constructing novel sbp operators from known quadrature rules to demonstrate the utility of the generalization the legendre gauss and legendre gauss radau quadrature points are used to construct sbp operators that do not include one or both boundary nodes

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

finite element exterior calculus from hodge theory to numerical stability this article reports on the confluence of two streams of research one emanating from the fields of numerical analysis and scientific computation the other from topology and geometry in it we consider the numerical discretization of partial differential equations that are related to differential complexes so that de rham cohomology and hodge theory are key tools for exploring the well posedness of the continuous problem the discretization methods we consider are finite element methods in which a variational or weak formulation of the pde problem is approximated by restricting the trial subspace to an appropriately constructed piecewise polynomial subspace after a brief introduction to finite element methods we develop an abstract hilbert space framework for analyzing the stability and convergence of such discretizations in this framework the differential complex is represented by a complex of hilbert spaces and stability is obtained by transferring hodgetheoretic structures that ensure well posedness of the continuous problem from the continuous level to the discrete we show stable discretization is achieved if the finite element spaces satisfy two hypotheses they can be arranged into a subcomplex of this hilbert complex and there exists a bounded cochain projection from that complex to the subcomplex in the next part of the paper we consider the most canonical example of the abstract theory in which the hilbert complex is the de rham complex of a domain in euclidean space we use the koszul complex to construct two families of finite element differential forms show that these can be arranged in subcomplexes of the de rham complex in numerous ways and for each construct a bounded cochain projection the abstract theory therefore applies to give the stability and convergence of finite element approximations of the hodge laplacian other applications are considered as well especially the elasticity complex and its application to the equations of elasticity background material is included to make the presentation self contained for a variety of readers

dirac structures and boundary control systems associated with skew symmetric differential operators associated with a skew symmetric linear operator on the spatial domain a b we define a dirac structure which includes the port variables on the boundary of this spatial domain this dirac structure is a subspace of a hilbert space naturally associated with this dirac structure is an infinite dimensional system we parameterize the boundary port variables for which the c 0 semigroup associated with this system is contractive or unitary furthermore this parameterization is used to split the boundary port variables into inputs and outputs similarly we define a linear port controlled hamiltonian system associated with the previously defined dirac structure and a symmetric positive operator defining the energy of the system we illustrate this theory on the example of the timoshenko beam

mixed mimetic spectral element method for stokes flow a pointwise divergence free solution in this paper we apply the recently developed mimetic discretization method to the mixed formulation of the stokes problem in terms of vorticity velocity and pressure the mimetic discretization presented in this paper and in kreeft et al 51 is a higher order method for curvilinear quadrilaterals and hexahedrals fundamental is the underlying structure of oriented geometric objects the relation between these objects through the boundary operator and how this defines the exterior derivative representing the grad curl and div through the generalized stokes theorem the mimetic method presented here uses the language of differential k forms with k cochains as their discrete counterpart and the relations between them in terms of the mimetic operators reduction reconstruction and projection the reconstruction consists of the recently developed mimetic spectral interpolation functions the most important result of the mimetic framework is the commutation between differentiation at the continuous level with that on the finite dimensional and discrete level as a result operators like gradient curl and divergence are discretized exactly for stokes flow this implies a pointwise divergence free solution this is confirmed using a set of test cases on both cartesian and curvilinear meshes it will be shown that the method converges optimally for all admissible boundary conditions

whitney forms of higher degree low order whitney elements are widely used for electromagnetic field problems higher order approximations are receiving increasing interest but their definition remains unduly complex in this paper we propose a new simple construction for whitney p elements of polynomial degree higher than one that use only degrees of freedom associated to p chains we provide a basis for these elements on simplicial meshes and give a geometrical localization of all degrees of freedom properties of the higher order whitney complex are deeply investigated

weak form of stokes dirac structures and geometric discretization of port hamiltonian systems we present the mixed galerkin discretization of distributed parameter port hamiltonian systems due to the inherent definition of boundary interconnection ports this system representation is particularly useful for the modeling of interconnected multi physics systems and control at the prototypical example of a system of two conservation laws in arbitrary spatial dimension we derive the main contributions i a weak formulation of the underlying geometric stokes dirac structure ii its geometric approximation by a finite dimensional dirac structure using a mixed galerkin approach and power preserving maps on the space of discrete power variables and iii the approximation of the hamiltonian to obtain finite dimensional port hamiltonian state space models the power preserving maps on the discrete bond space offer design degrees of freedom for the discretization which is illustrated at the example whitney finite elements on a 2d simplicial triangulation the resulting schemes can be considered as trade offs between centered approximations and upwinding

an error bound for a noise canceller the degradation in performance of the least mean square estimation lmse is evaluated after replacing the covariance matrices with estimates taking advantage of the statistical properties of the complex wishart matrix and its inverse the decrease in performance stemming from this substitution is investigated the performance criterion is based on the computation of the final output error which includes covariance deviations this is carried out for a certain class of linear observation models involving an underlying problem of noise cancelling using noise alone references nars namely array processing techniques using a known array manifold performance limits of the adaptive noise canceller are investigated for the case of a spectral filter to illustrate the ideas it is shown that its performance depends on the quadratic coherency between the corrupted signal and the nar it is preferable to run no processing when this coherency is not strong enough a rule is proposed in order to decide when to switch to the no processing scheme contrary to some previous results the results given are available without any approximations provided the statistical properties are satisfied in the case of a special noise canceller these properties are asymptotically satisfied in the case of a transversal noise canceller acting in the time domain these results are valid for white signals and noises

wavelet multigrid analysis of squeeze film characteristics of poroelastic bearings the combined study of effects of poroelasticity and couple stresses on the performance of lubrication aspects of porelastic bearings in general and that of synovial joints in particular are analyzed the modified form of reynolds equation which incorporates the elastic nature of cartilage and stokes couple stress fluid as lubricant is derived and solved using a recently developed wavelet multigrid method this method has greatest advantage of minimizing the errors using wavelet transforms in obtaining accurate solution as grid size tends to zero it is found that 6 7 cycles are required to obtain a reasonably accurate solution in the multigrid scheme whereas only one cycle is required to obtain the solution in the wavelet multigrid method also matrix of discrete wavelet transform acts as a natural preconditioner producing rapid convergence it is observed that the poroelastic bearings with couple stress fluid as lubricant provide enhancement in pressure and ensure the increased load carrying capacity compared with viscous fluids this may be one of the reasons in the efficient lubrication and proper functioning of synovial joints

noise reduction for an estimated wiener filter using noise references corresp a simple approach to the adaptation of a linear filter to cope with spectral uncertainties is presented based on the calculation of the total output error power including the errors of spectral estimation a criterion is proposed for deciding whether the estimated filter is effective at any given frequency by forcing the filter response to unity at all ineffective frequencies an improvement in performance is obtained

energy based lyapunov functions for forced hamiltonian systems with dissipation in this paper we propose a constructive procedure to modify the hamiltonian function of forced hamiltonian systems with dissipation in order to generate lyapunov functions for nonzero equilibria a key step in the procedure which is motivated from energy balance considerations standard in network modeling of physical systems is to embed the system into a larger hamiltonian system for which a series of casimir functions can be easily constructed interestingly enough for linear systems the resulting lyapunov function is the incremental energy thus our derivations provide a physical explanation to it an easily verifiable necessary and sufficient condition for the applicability of the technique in the general nonlinear case is given some examples that illustrate the method are given

a new multigrid approach to convection problems abstract a new multigrid method for convection problems is presented it is designed to overcome the problem of alignment the flow being aligned with the grid the technique employs semi coarsening in several directions simultaneously and gives rise to multiple coarser grids with the same total number of points per grid level but with different sizes in each co ordinate direction the amount of work per multigrid cycle is still o n as an example the method is applied to the nonlinear upwind differenced euler equations of gas dynamics in two dimensions convergence rates are estimated by two level fourier analysis for the linearised equations numerical experiments on the nonlinear equations confirm these estimates

spectral methods on arbitrary grids stable and spectrally accurate numerical methods are constructed on arbitrary grids for partial differential equations these new methods are equivalent to conventional spectral methods but do not rely on specific grid distributions specifically we show how to implement legendre galerkin legendre collocation and laguerre galerkin methodology on arbitrary grids

the frequency decomposition multilevel method a robust additive hierarchical basis preconditioner hackbusch s frequency decomposition multi level method is characterized by the application of three additional coarse grid corrections in parallel to the standard one each coarse grid correction was designed to damp errors from a different part of the frequency spectrum in this paper we introduce a cheap variant of this method partly based on semi coarsening which demands less recursive calls than the original version using the theory of the additive schwarz methods we will prove robustness of our method as a preconditioner applied to anisotropic equations

mixed finite elements for numerical weather prediction we show how mixed finite element methods that satisfy the conditions of finite element exterior calculus can be used for the horizontal discretisation of dynamical cores for numerical weather prediction on pseudo uniform grids this family of mixed finite element methods can be thought of in the numerical weather prediction context as a generalisation of the popular polygonal c grid finite difference methods there are a few major advantages the mixed finite element methods do not require an orthogonal grid and they allow a degree of flexibility that can be exploited to ensure an appropriate ratio between the velocity and pressure degrees of freedom so as to avoid spurious mode branches in the numerical dispersion relation these methods preserve several properties of the c grid method when applied to linear barotropic wave propagation namely a energy conservation b mass conservation c no spurious pressure modes and d steady geostrophic modes on the f plane we explain how these properties are preserved and describe two examples that can be used on pseudo uniform grids the recently developed modified rtk q k 1 element pairs on quadrilaterals and the bdfm1 p 1 dg element pair on triangles all of these mixed finite element methods have an exact 2 1 ratio of velocity degrees of freedom to pressure degrees of freedom finally we illustrate the properties with some numerical examples

a fast wavelet multigrid method to solve elliptic partial differential equations abstract in this paper we present a wavelet based multigrid approach to solve elliptic boundary value problems encountered in mathematical physics the system of equations arising from finite difference discretization is represented in wavelet basis these equations are solved using multiresolution properties of wavelets characterized by sparse matrices having condition number o 1 together with a multigrid strategy for accelerating convergence the filter coefficients of d 2 k k 2 3 4 from daubechies family of wavelets are used to demonstrate the effectiveness and efficiency of the method the distinguishing feature of the method is it works as both solver and preconditioner as a consequence it avoids instability minimizes error and speeds up convergence compared to the classical multigrid method this approach requires substantially shorter computation time at the same time meeting accuracy requirements it is found that just one cycle is enough for the convergence of wavelet multigrid scheme whereas normally 7 8 cycles are required in classical multigrid schemes to meet the same accuracy numerical examples show that the scheme offers a fast and robust technique for elliptic pde s

solving index 1 daes in matlab and simulink this paper describes mathematical and software developments needed for the effective solution of differential algebraic equations of index 1 in the integrated computing environment matlab and the dynamic simulation package simulink the developments are applicable to other problem solving environments and some are applicable to general scientific computation

fast and robust sixth order multigrid computation for the three dimensional convection diffusion equation we present a sixth order explicit compact finite difference scheme to solve the three dimensional 3d convection diffusion equation we first use a multiscale multigrid method to solve the linear systems arising from a 19 point fourth order discretization scheme to compute the fourth order solutions on both a coarse grid and a fine grid then an operator based interpolation scheme combined with an extrapolation technique is used to approximate the sixth order accurate solution on the fine grid since the multigrid method using a standard point relaxation smoother may fail to achieve the optimal grid independent convergence rate for solving convection diffusion equations with a high reynolds number we implement the plane relaxation smoother in the multigrid solver to achieve better grid independency supporting numerical results are presented to demonstrate the efficiency and accuracy of the sixth order compact soc scheme compared with the previously published fourth order compact foc scheme

port hamiltonian discretization for open channel flows a finite dimensional port hamiltonian formulation for the dynamics of smooth open channel flows is presented a numerical scheme based on this formulation is developed for both the linear and nonlinear shallow water equations the scheme is verified against exact solutions and has the advantage of conservation of mass and energy to the discrete level

fast algorithms for discrete time wiener filters with optimum lag in many applications including geophysical signal processing and system identification the computation of a fir wiener filter corresponding to the optimum lag between the input signal and the desired response or of an optimum prediction distance predictor are often required these problems lead to the solution of a family of toeplitz systems of equations having the same associated matrix but right hand side vectors which are shifted versions of each other a very efficient method for the solution of the optimum lag problem is the well known simpson s sideways recursions the purpose of this paper is to introduce two new algorithms for the efficient computation of the optimum lag wiener filter as well as the optimum prediction distance predictor their main characteristic is a coupled step down step up recursion which takes full advantage of both the toeplitz nature of the matrix and the shifted structure of the right hand side vectors the proposed algorithms are featured by increased speed they are about twice as fast as simpson s scheme and computational simplicity in addition they provide recursive error computation capability and give further insight into the problem

pseudo spectral methods for the spatial symplectic reduction of open systems of conservation laws a reduction method is presented for systems of conservation laws with boundary energy flow it is stated as a generalized pseudo spectral method which performs exact differentiation by using simultaneously several approximation spaces generated by polynomials bases and suitable choices of port variables the symplecticity of this spatial reduction method is proved when used for the reduction of both closed and open systems of conservation laws for any choice of collocation points i e for any polynomial bases the symplecticity of some more usual collocation schemes is discussed and finally their accuracy on approximation of the spectrum on the example of the ideal transmission line is discussed in comparison with the suggested reduction scheme

a gmres based plane smoother in multigrid to solve 3d anisotropic fluid flow problems for a discretization of the 3d steady incompressible navier stokes equations a solution method is presented for solving flow problems on stretched grids the discretization is a vertex centered finite volume discretization with a flux splitting approach for the convective terms second order accuracy is obtained with the well known defect correction technique b koren j comput phys 87 25 1990 the solution method used is multigrid for which a plane smoother is presented for obtaining good convergence in flow domains with severely stretched grids a matrix is set up in a plane which is solved iteratively with a preconditioned gmres method here a stop criterion for gmres is tested which reduces the number of inner iterations compared to an exact plane solver without affecting the multigrid convergence rates the performance of the solution method is shown for a poisson model problem and for 3d incompressible channel flow examples

direct multi grid methods for linear systems with harmonic aliasing patterns multi level numerical methods that obtain the exact solution of a linear system are presented the methods are devised by combining ideas from the full multi grid algorithm and perfect reconstruction filters the problem is stated as whether a direct solver is possible in a full multi grid scheme by avoiding smoothing iterations and using different coarse grids at each step the coarse grids must form a partition of the fine grid and thus establishes a strong connection with domain decomposition methods an important analogy is established between the conditions for direct solution in multi grid solvers and perfect reconstruction in filter banks furthermore simple solutions of these conditions for direct multi grid solvers are found by using mirror filters as a result different configurations of direct multi grid solvers are obtained and studied

a new multigrid formulation for high order finite difference methods on summation by parts form multigrid schemes for high order finite difference methods on summation by parts form are studied by comparing the effect of different interpolation operators by using the standard linear prolonga

dirac structures on hilbert spaces and boundary control of distributed port hamiltonian systems abstract aim of this paper is to show how the dirac structure properties can be exploited in the development of energy based boundary control laws for distributed port hamiltonian systems usually stabilization of non zero equilibria has been achieved by looking at or generating a set of structural invariants namely casimir functions in closed loop since this approach fails when an infinite amount of energy is required at the equilibrium dissipation obstacle this paper illustrates a novel approach that enlarges the class of stabilizing controllers the starting point is the parametrization of the dynamics provided by the image representation of the dirac structure that is able to show the effects of the boundary inputs on the state evolution in this way energy balancing and control by state modulated source methodologies are extended to the distributed parameter scenario and a geometric interpretation of these control techniques is provided the theoretical results are discussed with the help of a simple but illustrative example i e a transmission line with an rlc load in both serial and parallel configurations in the latter case energy balancing controllers are not able to stabilize non zero equilibria because of the dissipation obstacle the problem is solved thanks to a boundary state modulated source

a unified approach to energy conservation and potential vorticity dynamics for arbitrarily structured c grids a numerical scheme applicable to arbitrarily structured c grids is presented for the nonlinear shallow water equations by discretizing the vector invariant form of the momentum equation the relationship between the nonlinear coriolis force and the potential vorticity flux can be used to guarantee that mass velocity and potential vorticity evolve in a consistent and compatible manner underpinning the consistency and compatibility of the discrete system is the construction of an auxiliary thickness equation that is staggered from the primary thickness equation and collocated with the vorticity field the numerical scheme also exhibits conservation of total energy to within time truncation error simulations of the standard shallow water test cases confirm the analysis and show convergence rates between 1st and 2nd order accuracy when discretizing the system with quasi uniform spherical voronoi diagrams the numerical method is applicable to a wide class of meshes including latitude longitude grids voronoi diagrams delaunay triangulations and conformally mapped cubed sphere meshes

the chebyshev legendre method implementing legendre methods on chebyshev points a new collocation method for the numerical solution of partial differential equations is presented this method uses the chebyshev collocation points but because of the way the boundary conditions are implemented it has all the advantages of the legendre methods in particular l 2 estimates can be easily obtained for hyperbolic and parabolic problems

on representations and integrability of mathematical structures in energy conserving physical systems in the present paper we elaborate on the underlying hamiltonian structure of interconnected energy conserving physical systems it is shown that a power conserving interconnection of port controlled generalized hamiltonian systems leads to an implicit generalized hamiltonian system and a power conserving partial interconnection to an implicit port controlled hamiltonian system the crucial concept is the notion of a generalized dirac structure defined on the space of energy variables or on the product of the space of energy variables and the space of flow variables in the port controlled case three natural representations of generalized dirac structures are treated necessary and sufficient conditions for closedness or integrability of dirac structures in all three representations are obtained the theory is applied to implicit port controlled generalized hamiltonian systems and it is shown that the closedness condition for the dirac structure leads to strong conditions on the input vector fields

a finite element exterior calculus framework for the rotating shallow water equations we describe discretisations of the shallow water equations on the sphere using the framework of finite element exterior calculus which are extensions of the mimetic finite difference framework presented in ringler 2010 11 the exterior calculus notation provides a guide to which finite element spaces should be used for which physical variables and unifies a number of desirable properties we present two formulations a primal formulation in which the finite element spaces are defined on a single mesh and a primal dual formulation in which finite element spaces on a dual mesh are also used both formulations have velocity and layer depth as prognostic variables but the exterior calculus framework leads to a conserved diagnostic potential vorticity in both formulations we show how to construct discretisations that have mass consistent constant potential vorticity stays constant stable and oscillation free potential vorticity advection

a new method for d dimensional exact deconvolution deconvolution is an important problem of signal processing and conventional approaches including fourier methods have stability problems due to the zeros of the convolution kernel we present a new method of multidimensional exact deconvolution this method is always stable even when the convolution kernel h n has zeros on the unit circle and there exist closed form solutions for the one dimensional 1 d case d 1 for the multidimensional case d 1 the proposed method yields stable solutions when det h d this solution set covers a portion of all possible convolution kernels including the ones that have zeros on the multidimensional unit circle this novel time domain method is based on the fact that the convolution inverse of a first order kernel can be found exactly in multidimensional space convolution inverses for higher order kernels are obtained using this fact and the zeros of the convolution kernel the presented method is exact stable and computationally efficient several examples are given in order to show the performance of this method in 1 d and multidimensional cases

stability and passivity preserving petrov galerkin approximation of linear infinite dimensional systems this contribution presents two approximation methods for linear infinite dimensional systems that ensure the preservation of stability and passivity the first approach allows one to approximate internal source free infinite dimensional systems such that the resulting approximation is a port controlled hamiltonian system with dissipation the second method deals with the class of systems that are not required to have conjugated outputs but only a dissipative system operator it yields approximations with a dissipative system matrix for which bounds of their stability margin are provided both approaches are based on a state space formulation of the infinite dimensional system this makes it possible to use the petrov galerkin approximation whose free parameters are partly used for achieving the structure preservation since still free parameters remain further application specific objectives such as e g moment matching can be achieved both approaches are applied to the approximation of an euler bernoulli beam

certifying spatially uniform behavior in reaction diffusion pde and compartmental ode systems we present a condition that guarantees spatial uniformity for the asymptotic behavior of the solutions of a reaction diffusion pde with neumann boundary conditions this condition makes use of the jacobian matrix of the reaction terms and the second neumann eigenvalue of the laplacian operator on the given spatial domain and eliminates the global lipschitz assumptions commonly used in mathematical biology literature we then derive numerical procedures that employ linear matrix inequalities to certify this condition and illustrate these procedures on models of several biochemical reaction networks finally we present an analog of this pde result for the synchronization of a network of identical ode models coupled by diffusion terms from a systems biology perspective the main contribution of the paper is to blend analytical and numerical tools from nonlinear systems and control theory to derive a relaxed and verifiable condition for spatial uniformity of biological processes

achievable casimirs and its implications on control of port hamiltonian systems in this paper we extend results on interconnections of port hamiltonian systems to infinite dimensional port hamiltonian systems and to mixed finite and infinite dimensional port hamiltonian systems the problem of achievable dirac structures is now studied for systems with dissipation in the finite dimensional infinite dimensional and the mixed finite and infinite dimensional case we also characterize the set of achievable casimirs and study its application for the control of port hamiltonian systems

the improved robustness of multigrid elliptic solvers based on multiple semicoarsened grids multigrid convergence rates degenerate on problems with stretched grids or anisotropic operators unless one uses line or plane relaxation for three dimensional problems only plane relaxation suffices in general while line and plane relaxation algorithms are efficient on sequential machines they are quite awkward and inefficient on parallel machines this paper presents a new multigrid algorithm based on the use of multiple coarse grids that eliminates the need for line or plane relaxation in anisotropic problems this algorithm is developed and the standard multigrid theory is extended to establish rapid convergence for this class of algorithms the new algorithm uses only point relaxation allowing easy and efficient parallel implementation yet achieves robustness and convergence rates comparable to line and plane relaxation multigrid algorithms the algorithm described here is a variant of mulder s multigrid algorithm w mulder j compact phys 83 1989 pp 303 323 for hyperbolic problem

structure preserving moment matching for port hamiltonian systems arnoldi and lanczos structure preserving model reduction of single input single output port hamiltonian systems is considered by employing the rational krylov methods the rational arnoldi method is shown to preserve for the reduced order model not only a specific number of the moments at an arbitrary point in the complex plane but also the port hamiltonian structure furthermore it is shown how the rational lanczos method applied to a subclass of port hamiltonian systems characterized by an algebraic condition preserves the port hamiltonian structure in fact for the same subclass of port hamiltonian systems the rational arnoldi method and the rational lanczos method turn out to be equivalent in the sense of producing reduced order port hamiltonian models with the same transfer function

flexible multiple semicoarsening for three dimensional singularly perturbed problems we present robust parallel multigrid based solvers for 3d scalar partial differential equations the robustness is obtained by combining multiple semicoarsening strategies matrix dependent transfer operators and a krylov subspace acceleration the basis for the 3d preconditioner is a 2d method with multiple semicoarsened grids based on the mg s method from c w oosterlee appl numer math 19 1995 pp 115 128 and t washio and c w oosterlee gmd arbeitspapier 949 gmd st augustin germany 1995 the 2d method is generalized to three dimensions with a line smoother in the third dimension the method based on semicoarsening has been parallelized with the grid partitioning technique j linden b steckel and k stuben parallel comput 7 1988 pp 461 475 o a mcbryan et al impact comput sci engrg 3 1991 pp 1 75 and is evaluated as a solver and as a preconditioner on a mimd machine the robustness of the 3d method is shown for finite volume and finite difference discretizations of 3d anisotropic diffusion equations and convection dominated convection diffusion problems

discretely conservative finite difference formulations for nonlinear conservation laws in split form theory and boundary conditions the lax wendroff theorem stipulates that a discretely conservative operator is necessary to accurately capture discontinuities the discrete operator however need not be derived from the divergence form of the continuous equations indeed conservation law equations that are split into linear combinations of the divergence and product rule form and then discretized using any diagonal norm skew symmetric summation by parts sbp spatial operator yield discrete operators that are conservative furthermore split form discretely conservation operators can be derived for periodic or finite domain sbp spatial operators of any order examples are presented of a fourth order sbp finite difference operator with second order boundary closures sixth and eighth order constructions are derived and are supplied in an accompanying text file

modeling and control of the timoshenko beam the distributed port hamiltonian approach the purpose of this paper is to show how the timoshenko beam can be fruitfully described within the framework of distributed port hamiltonian dph systems so that rather simple and elegant considerations can be drawn regarding both the modeling and control of this mechanical system after the dph model of the beam is introduced the control problem is discussed in particular it is shown how control approaches already presented in the literature can be unified and a new control methodology is presented and discussed this control methodology relies on the generalization to infinite dimensions of the concept of structural invariant casimir function and on the extension to distributed systems of the so called control by interconnection methodology in this way finite dimensional passive controllers can stabilize distributed parameter systems by shaping their total energy i e by assigning a new minimum in the desired equilibrium configuration that can be reached if a dissipative effect is introduced

well posed and stable transmission problems we introduce the notion of a transmission problem to describe a general class of problems where different dynamics are coupled in time well posedness and stability is analysed for continuous and d

a port hamiltonian formulation of the navier stokes equations for reactive flows abstract we consider the problem of finding an energy based formulation of the navier stokes equations for reactive flows these equations occur in various applications e g in combustion engines or chemical reactors after modeling discretization and model reduction important system properties as the energy conservation are usually lost which may lead to unphysical simulation results in this paper we introduce a port hamiltonian formulation of the one dimensional navier stokes equations for reactive flows the port hamiltonian structure is directly associated with an energy balance which ensures that a temporal change of the total energy is only due to energy flows through the boundary furthermore the boundary ports may be used for control purposes

an energy minimizing interpolation for robust multigrid methods we propose a robust interpolation for multigrid based on the concepts of energy minimization and approximation it can handle pde coefficients of various types on structured or unstructured grids under one framework the formulation is general it can be applied to any dimension we demonstrate numerically the effectiveness of the multigrid method in two dimensions by applying it to a discontinuous coefficient problem an oscillatory coefficient problem and an anisotropic problem empirically the convergence rate is independent of the coefficients of the underlying pde in addition to being independent of the mesh size the proposed method is primarily designed for second order elliptic pdes with possible extensions to other classes of problems such as integral equations

building systems from simple hyperbolic ones in this article we introduce a technique that derives from the existence and uniqueness of solutions to a simple hyperbolic partial differential equation p d e the existence and uniqueness of solutions to hyperbolic and parabolic p d e s among others we show that starting with an impedance passive system associated to the undamped wave equation we can obtain an impedance passive system associated to the heat conduction equation

energy shaping of distributed parameter port hamiltonian systems based on finite element approximation the main contribution of this paper is a procedure for the control by energy shaping via casimir generation of infinite dimensional port hamiltonian systems based on a particular finite element approximation the proposed approach is justified by the fact that the adopted spatial discretization technique is able to preserve casimir functions in the closed loop system when going from the distributed to the approximated lumped parameter system besides the intrinsic difficulties related to the large number of state variables the finite element model is generally given in terms of a dirac structure and is completely a causal which implies that the plant dynamics is not given in standard input state output form but as a set of daes consequently the classical energy casimir method has to be extended in order to deal with dynamical systems with constraints usually appearing in the form of lagrangian multipliers the general methodology is illustrated with the help of an example in which the distributed parameter system is a lossless transmission line

a passivity based approach to stability of spatially distributed systems with a cyclic interconnection structure a class of distributed systems with a cyclic interconnection structure is considered these systems arise in several biochemical applications and they can undergo diffusion driven instability which leads to a formation of spatially heterogeneous patterns in this paper a class of cyclic systems in which addition of diffusion does not have a destabilizing effect is identified for these systems global stability results hold if the ldquosecantrdquo criterion is satisfied in the linear case it is shown that the secant condition is necessary and sufficient for the existence of a decoupled quadratic lyapunov function which extends a recent diagonal stability result to partial differential equations for reaction diffusion equations with nondecreasing coupling nonlinearities global asymptotic stability of the origin is established all of the derived results remain true for both linear and nonlinear positive diffusion terms similar results are shown for compartmental systems

on additive schwarz preconditioners for sparse grid discretizations based on the framework of subspace splitting and the additive schwarz scheme we give bounds for the condition number of multilevel preconditioners for sparse grid discretizations of elliptic model problems for a bxp like preconditioner we derive an estimate of the optimal ordero 1 and for a hb like variant we obtain an estimate of the ordero k 2 2 k 2 wherek denotes the number of levels employed furthermore we confirm these results by numerically computed condition numbers

a multigrid method for the helmholtz equation with optimized coarse grid corrections we study the convergence of multigrid schemes for the helmholtz equation focusing in particular on the choice of the coarse scale operators let g rm c denote the number of points per wavelength at the coarse level if the coarse scale solutions are to approximate the true solutions then the oscillatory nature of the solutions implies the requirement g rm c 2 however in examples the requirement is more like g rm c gtrsim 10 in a trade off involving also the amount of damping present and the number of multigrid iterations we conjecture that this is caused by the difference in phase speeds between the coarse and fine scale operators standard 5 point finite differences in two dimensions are our first example a new coarse scale 9 point operator is constructed to match the fine scale phase speeds we then compare phase speeds and multigrid performance of standard schemes with a scheme using the new operator the required g rm c is reduced from about 10 to about 3 5 with less dam

on the order of prolongations and restrictions in multigrid procedures abstract it is well known in the world of multigrid that the order of the prolongation and the order of the restriction in a multigrid method should satisfy certain conditions a rule of thumb is that the sum of the orders of the prolongation and of the restriction should at least be equal to the order of the differential equation solved in this note we show the correctness of this rule we notice that we have to distinguish between low frequency and high frequency orders for the transfer operators for the restriction the low frequency order is related with its accuracy whereas for the interpolation operator both orders are related with the accuracy of the result of the interpolation if an interpolation rule leaves all polynomials of degree k 1 invariant then both the low and the high frequency order are equal to k it is the high frequency order that plays a role in the above mentioned rule of thumb

inverse filtering of room acoustics a novel method is proposed for realizing exact inverse filtering of acoustic impulse responses in room this method is based on the principle called the multiple input output inverse theorem mint the inverse is constructed from multiple finite impulse response fir filters transversal filters by adding some extra acoustic signal transmission channels produced by multiple loudspeakers or microphones the coefficients of these fir filters can be computed by the well known rules of matrix algebra inverse filtering in a sound field is investigated experimentally it is shown that the proposed method is greatly superior to previous methods that use only one acoustic signal transmission channel the results prove the possibility of sound reproduction and sound reception without any distortion caused by reflected sounds

dirac structures and their composition on hilbert spaces dirac structures appear naturally in the study of certain classes of physical models described by partial differential equations and they can be regarded as the underlying power conserving structures we study these structures and their properties from an operator theoretic point of view in particular we find necessary and sufficient conditions for the composition of two dirac structures to be a dirac structure and we show that they can be seen as lagrangian hyper maximal neutral subspaces of krein spaces moreover special emphasis is laid on dirac structures associated with operator colligations it turns out that this class of dirac structures is linked to boundary triplets and that this class is closed under composition

distributed algorithms for reaching consensus on general functions this paper presents analysis and design results for distributed consensus algorithms in multi agent networks we consider continuous consensus functions of the initial state of the network agents under mild smoothness assumptions we obtain necessary and sufficient conditions characterizing any algorithm that asymptotically achieves consensus this characterization is the building block to obtain various design results for networks with weighted directed interconnection topologies we first identify a class of smooth functions for which one can synthesize in a systematic way distributed algorithms that achieve consensus we apply this result to the family of weighted power mean functions and characterize the exponential convergence properties of the resulting algorithms we establish the validity of these results for scenarios with switching interconnection topologies finally we conclude with two discontinuous distributed algorithms that achieve respectively max and min consensus in finite time

on structure preserving model reduction for damped wave propagation in transport networks we consider the discretization and subsequent model reduction of a system of partial differential algebraic equations describing the propagation of pressure waves in a pipeline network important properties like conservation of mass dissipation of energy passivity existence of steady states and exponential stability can be preserved by an appropriate semidiscretization in space via a mixed finite element method and also during the further dimension reduction by structure preserving galerkin projection which is the main focus of this paper krylov subspace methods are employed for the construction of the reduced models and we discuss certain modifications needed to satisfy some algebraic compatibility conditions which are required to ensure the well posedness of the reduced models and the preservation of the key properties our arguments are based on a careful analysis of the underlying infinite dimensional problem and its galerkin approximations the proposed algorithms therefore have a direct inte

robust multigrid methods for nonsmooth coefficient elliptic linear systems we survey the literature on robust multigrid methods which have been developed in recent years for solving second order elliptic pdes with nonsmooth coefficients we highlight the key ideas of designing robust multigrid methods which are able to recover the usual multigrid efficiency for nonsmooth coefficient pdes on structured or unstructured grids in particular we shall describe various approaches for constructing the interpolation and the smoothing operators and the coarse grid points selections

correction to structure and stability of certain chemical networks and applications to the kinetic proofreading model of t cell receptor signal transduction deals with the theory of structure stability robustness and stabilization for an appealing class of nonlinear systems which arises in the analysis of chemical networks the results given here extend but are also heavily based upon certain previous work by feinberg 1977 1979 1987 1995 and horn and jackson 1972 of which a self contained and streamlined exposition is included the theoretical conclusions are illustrated through an application to the kinetic proofreading model proposed by mckeithan 1995 for t cell receptor signal transduction

port hamiltonian systems on graphs in this paper we present a unifying geometric and compositional framework for modeling complex physical network dynamics as port hamiltonian systems on open graphs the basic idea is to associate with the incidence matrix of any directed graph a dirac structure relating the flow and effort variables associated to the edges and vertices of the graph and to formulate energy storing or energy dissipating relations between the flow and effort variables of the edges and the internal vertices this allows for state variables associated to the edges and formalizes the interconnection of networks examples from different origins such as consensus algorithms that share the same structure are shown it is shown how the identified hamiltonian structure offers systematic tools for the analysis and control of the resulting dynamics

a spectral element method for fluid dynamics laminar flow in a channel expansion a spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible navier stokes equations in the spectral element discretization the computational domain is broken into a series of elements and the velocity in each element is represented as a high order lagrangian interpolant through chebyshev collocation points the hyperbolic piece of the governing equations is then treated with an explicit collocation scheme while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle the implementation of the technique is demonstrated on a one dimensional inflow outflow advection diffusion equation and the method is then applied to laminar two dimensional separated flow in a channel expansion comparisons are made with experiment and previous numerical work

a hamiltonian vorticity dilatation formulation of the compressible euler equations using the hodge decomposition on bounded domains the compressible euler equations of gas dynamics are reformulated using a density weighted vorticity and dilatation as primary variables together with the entropy and density this formulation is an extension to compressible flows of the well known vorticity stream function formulation of the incompressible euler equations the hamiltonian and associated poisson bracket for this new formulation of the compressible euler equations are derived and extensive use is made of differential forms to highlight the mathematical structure of the equations in order to deal with domains with boundaries also the stokes dirac structure and the port hamiltonian formulation of the euler equations in density weighted vorticity and dilatation variables are obtained

the frequency decomposition multi grid method ii convergence analysis based on the additive schwarz method the convergence analysis of a special variant of the additive schwarz iteration is presented it can be applied to the frequency decomposition multigrid method and yields robust convergence

hamiltonian discretization of boundary control systems a fundamental problem in the simulation and control of complex physical systems containing distributed parameter components concerns finite dimensional approximation numerical methods for partial differential equations pdes usually assume the boundary conditions to be given while more often than not the interaction of the distributed parameter components with the other components takes place precisely via the boundary on the other hand finite dimensional approximation methods for infinite dimensional input output systems e g in semi group format are not easily relatable to numerical techniques for solving pdes and are mainly confined to linear pdes in this paper we take a new view on this problem by proposing a method for spatial discretization of boundary control systems based on a particular type of mixed finite elements resulting in a finite dimensional input output system the approach is based on formulating the distributed parameter component as an infinite dimensional port hamiltonian system and exploiting the geometric structure of this representation for the choice of appropriate mixed finite elements the spatially discretized system is again a port hamiltonian system which can be treated as an approximating lumped parameter physical system of the same type in the current paper this program is carried out for the case of an ideal transmission line described by the telegrapher s equations and for the two dimensional wave equation

wavelet deconvolution this paper studies the issue of optimal deconvolution density estimation using wavelets the approach taken here can be considered as orthogonal series estimation in the more general context of the density estimation we explore the asymptotic properties of estimators based on thresholding of estimated wavelet coefficients minimax rates of convergence under the integrated square loss are studied over besov classes b sub spl sigma pq of functions for both ordinary smooth and supersmooth convolution kernels the minimax rates of convergence depend on the smoothness of functions to be deconvolved and the decay rate of the characteristic function of convolution kernels it is shown that no linear deconvolution estimators can achieve the optimal rates of convergence in the besov spaces with p 2 when the convolution kernel is ordinary smooth and super smooth if the convolution kernel is ordinary smooth then linear estimators can be improved by using thresholding wavelet deconvolution estimators which are asymptotically minimax within logarithmic terms adaptive minimax properties of thresholding wavelet deconvolution estimators are also discussed

a robust hierarchical basis preconditioner on general meshes in this paper we introduce a multi level direct sum space decomposition of general possibly locally refined linear or multi linear finite element spaces the resulting additive schwarz preconditioner is optimal for symmetric second order elliptic problems moreover it turns out to be robust with respect to coefficient jumps over edges in the coarsest mesh perturbations with positive zeroth order terms and after a further decomposition of the spaces also with respect to anisotropy along the grid lines important for an efficient implementation is that stable bases of the subspaces defining our decomposition consisting of functions having small supports can be easily constructed

lse and mse optimum partition based fir iir deconvolution filters with best delay we considered the least squares error lse and mean square error mse optimum best delay deconvolution filter design we presented the partition based finite impulse response infinite impulse response fir iir filters where the channel zeros are partitioned into two regions the first region is composed of the selected channel zeros inside the unit circle and the second region is composed of the remaining channel zeros outside the first region two methods for obtaining partitions are proposed namely optimum partitioning and ring based partitioning resulting fir iir filters are compared with the fir and fir iir unit circle best delay inverse filters in terms of their lse it is shown that the partition based fir iir filter performances are about 4 5 db better than their fir counterpart for the same complexity then starting with the best delay fir wiener deconvolution filter formulation we extended our results for the design of fir iir mse optimum deconvolution filters we have compared the optimum partitioning and ring based fir iir inverse filters with the fir and iir wiener deconvolution filters it is shown that fir iir best delay inverse filters are less sensitive to the estimation errors compared with the iir wiener filters and they perform better than the fir wiener filters furthermore they are always causal and stable making them suitable for real time implementations

optimality of high resolution array processing using the eigensystem approach in the classical approach to underwater passive listening the medium is sampled in a convenient number of look directions from which the signals are estimated in order to build an image of the noise field in contrast a modern trend is to consider the noise field as a global entity depending on few parameters to be estimated simultaneously in a gaussian context it is worthwhile to consider the application of likelihood methods in order to derive a detection test for the number of sources and estimators for their locations and spectral levels this paper aims to compute such estimators when the wavefront shapes are not assumed known a priori this justifies results previously found using the asymptotical properties of the eigenvalue eigenvector decomposition of the estimated spectral density matrix of the sensor signals they have led to a variety of high resolution array processing methods more specifically a covariance matrix test for equality of the smallest eigenvalues is presented for source detection for source localization a best fit method and a test of orthogonality between the smallest eigenvectors and the source vectors are discussed

a boundary condition capturing multigrid approach to irregular boundary problems we propose a geometric multigrid method for solving linear systems arising from irregular boundary problems involving multiple interfaces in two and three dimensions in this method we adopt a matrix free approach i e we do not form the fine grid matrix explicitly and we never form nor store the coarse grid matrices as many other robust multigrid methods do the main idea is to construct an accurate interpolation which captures the correct boundary conditions at the interfaces via a level set function numerical results are given to compare our multigrid method with black box and algebraic multigrid methods

control by interconnection of mixed port hamiltonian systems in this note the regulation problem for mixed finite and infinite dimensional port hamiltonian systems m ph systems is discussed a m ph system results from the power conserving interconnection of finite and infinite dimensional systems in port hamiltonian form in particular the system given by the interconnection of two finite dimensional systems one of which is the controller by means of an infinite dimensional connection is studied the proposed control methodology is a generalization to the infinite dimensional case of a well established passivity based control technique for finite dimensional port hamiltonian systems the control by interconnection and energy shaping according to which the open loop energy function is shaped so that a minimum in the desired configuration is introduced this procedure is possible once the state variable of the controller is related to the state variable of the plant by constraining the state of the closed loop system on a structural invariant defined by a set of casimir functions in this way the energy function of the controller which is freely assignable becomes a function of the configuration of the plant and then it can be easily shaped in order to solve the regulation problem

jet bundle formulation of infinite dimensional port hamiltonian systems using differential operators we consider infinite dimensional port hamiltonian systems described on jet bundles based on a power balance relation we introduce the port hamiltonian system representation using differential operators regarding the structural mapping the dissipation mapping and the input mapping in contrast to the well known representation on the basis of the underlying stokes dirac structure our approach is not necessarily based on using energy variables which leads to a different port hamiltonian representation of the analyzed partial differential equations the presented constructions will be specialized to mechanical systems to which class also the presented examples belong

improved boundary conditions for viscous reacting compressible flows previous studies on physical boundary conditions for flame boundary interactions of an ideal multicomponent compressible gas have neglected reactive source terms in their boundary condition treatments by combining analyses of incompletely parabolic systems with those based on the hyperbolic euler equations a rational set of boundary conditions is determined to address this shortcoming accompanying these conditions is a procedure for implementation into a maltidimensional code in the limits of zero reaction rate or one species the boundary conditions reduce in a predictable way to cases found in the literature application is made to premixed and nonpremixed flames in one and two dimensions to establish efficacy inclusion of source terms in boundary conditions derived from characteristic analysis is essential to avoid unphysical generation of pressure and velocity gradients as well as flow reversals minor deficiencies in the boundary conditions are attributed primarily to the diffusive terms imposing vanishing diffusive boundary normal flux gradients works better than imposing vanishing fluxes but neither is entirely satisfactory