scaling variables and asymptotic expansions in damped wave equations abstract we study the long time behavior of small solutions to the nonlinear damped wave equationeu u a u n u u u r 0 whereeis a positive not necessarily small parameter we assume that the diffusion coefficienta converges to positive limitsa as and that the nonlinearity n u u u vanishes sufficiently fast asu 0 introducing scaling variables and using various energy estimates we compute an asymptotic expansion of the solutionu in powers of 1 2as and we show that this expansion is entirely determined up to the second order by a linear parabolic equation which depends only on the limiting valuesa in particular this implies that the small solutions of the damped wave equation behave for large like those of the parabolic equation obtained by settinge 0

efficient nonlinear solvers for laplace beltrami smoothing of three dimensional unstructured grids the laplace beltrami system of nonlinear elliptic partial differential equations has utility in the generation of computational grids on complex and highly curved geometry discretization of this system using the finite element method accommodates unstructured grids but generates a large sparse ill conditioned system of nonlinear discrete equations the use of the laplace beltrami approach particularly in large scale applications has been limited by the scalability and efficiency of solvers this paper addresses this limitation by developing two nonlinear solvers based on the jacobian free newton krylov jfnk methodology a key feature of these methods is that the jacobian is not formed explicitly for use by the underlying linear solver iterative linear solvers such as the generalized minimal residual gmres method do not technically require the stand alone jacobian instead its action on a vector is approximated through two nonlinear function evaluations the preconditioning required by gmres is also discussed two different preconditioners are developed both of which employ existing algebraic multigrid amg methods further the most efficient preconditioner overall for the problems considered is based on a picard linearization numerical examples demonstrate that these solvers are significantly faster than a standard newton krylov approach a speedup factor of approximately 26 was obtained for the picard preconditioner on the largest grids studied here in addition these jfnk solvers exhibit good algorithmic scaling with increasing grid size

on level set regularization for highly ill posed distributed parameter estimation problems the recovery of a distributed parameter function with discontinuities from inverse problems with elliptic forward pdes is fraught with theoretical and practical difficulties better results are obtained for problems where the solution may take on at each point only one of two values thus yielding a shape recovery problem this article considers level set regularization for such problems however rather than explicitly integrating a time embedded pde to steady state which typically requires thousands of iterations methods based on gauss newton are applied more directly one of these can be viewed as damped gauss newton utilized to approximate the steady state equations which in turn are viewed as the necessary conditions of a tikhonov type regularization with a sharpening sub step at each iteration in practice this method is eclipsed however by a special finite time or levenberg marquardt type method which we call dynamic regularization applied to the output least squares formulation our stopping criterion for the iteration does not involve knowledge of the true solution the regularization functional is applied to the smooth level set function rather than to the discontinuous function to be recovered and the second focus of this article is on selecting this functional typical choices may lead to flat level sets that in turn cause ill conditioning we propose a new quartic non local regularization term that penalizes flatness and produces a smooth level set evolution and compare its performance to more usual choices two numerical test cases are considered a potential problem and the classical eit dc resistivity problem

critical exponents for semilinear dissipative wave equations in rn abstract we shall present new critical exponents 1 2m n with m 1 2 to the cauchy problem utt u ut u p 1u with the initial data u 0 u 1 h 1 r n l m r n l 2 r n l m r n that is the small data global existence property can be derived to the cauchy problem above with power 1 2m n

critical exponent for semilinear damped wave equations in the n dimensional half space abstract we generalize a previous result of ikehata math methods appl sci in press which studies the critical exponent problem of a semilinear damped wave equation in the one dimensional half space to the general n dimensional half space case that is to say one can show the small data global existence of solutions of a mixed problem for the equation utt u ut u p with the power p satisfying p n 1 2 n 1 if we deal with the problem in the n dimensional half space

the role of critical exponents in blow up theorems the sequel abstract in 27 fujita showed that for positive solutions the initial value problem in r n for u t u u p with p 1 exhibited the following behavior if p p c 1 2 n then the initial value problem does not have any nontrivial non negative solution existing on r n 0 a global solution whereas if p p c there exist global small data positive solutions as well as solutions which are non global we call such a result a blow up theorem of fujita type in 50 levine discussed the various theorems of this type that had appeared in the literature prior to 1990 in this paper we revisit the literature since 1990

an augmented lagrangian method for identifying discontinuous parameters in elliptic systems the identification of discontinuous parameters in elliptic systems is formulated as a constrained minimization problem combining the output least squares and the equation error method the minimization problem is then proved to be equivalent to the saddle point problem of an augmented lagrangian the finite element method is used to discretize the saddle point problem and the convergence of the discretization is also proved finally an uzawa algorithm is suggested for solving the discrete saddle point problem and is shown to be globally convergent

average adjacencies for tetrahedral skeleton regular partitions for any conforming mesh the application of a skeleton regular partition over each element in the mesh produces a conforming mesh such that all the topological elements of the same dimension are subdivided into the same number of child elements every skeleton regular partition has associated special constitutive recurrence equations in this paper the average adjacencies associated with the skeleton regular partitions in 3d are studied in three dimensions different values for the asymptotic number of average adjacencies are obtained depending on the considered partition in contrast with the two dimensional case j comput appl math 140 2002 673 in addition a priori formulae for the average asymptotic adjacency relations for any skeleton regular partition in 3d are provided

asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy we study the asymptotic time behavior of global smooth solutions to general entropy dissipative hyperbolic systems of balance law in m space dimensions under the shizuta kawashima condition we show that these solutions approach constant equilibrium state in the lp norm at a rate o t m 2 1 1 p as t tends to infty for p in min m 2 infty moreover we can show that we can approximate with a faster order of convergence theconservative part of the solution in terms of the linearized hyperbolic operator for m 2 and by a parabolic equation in the spirit of chapman enskog expansion the main tool is given by a detailed analysis of the green function for the linearized problem

on the recovery of multiple flow parameters from transient head data the problem of estimating groundwater flow parameters from head measurements and other ancillary data is fundamental to the process of modelling a groundwater system we consider here a new method that allows for the simultaneous computation of multiple parameters as the unique minimum of a convex functional

damped wave equation in the subcritical case abstract we study large time asymptotics of small solutions to the cauchy problem for the one dimensional nonlinear damped wave equation 1 v tt v t v xx v 1 0 x r t 0 v 0 x v 0 x v t 0 x v 1 x in the sub critical case 2 3 2 we assume that the initial data v 0 1 x 1 v 1 l l 1 a a 0 1 where l 1 a l 1 l 1 a a l 1 x 1 x 2 also we suppose that the mean value of initial data r v 0 x v 1 x dx 0 then there exists a positive value such that the cauchy problem 1 has a unique global solution v t x c 0 l l 1 a satisfying the following time decay estimate v t l c t 1 for large t 0 here 2 3 2

an optimal estimate for the difference of solutions of two abstract evolution equations abstractikehata and nishihara have established that the difference between any solution u of alinearly damped abstract wave equation and a certain solution v of a related abstract heatequation decays at least like t 1 logt 12 e as time tends to in nity they conjectured that thedecayisinfactliket 1 weproveherethevalidityofthisconjecturebyrelyingonthespectraltheorem for unbounded self adjoint operators we also establish the optimality of thisestimate for the wave equation in an exterior domain r 2003 elsevier science usa all rights reserved msc primary34d05 secondary35l90keywords abstract heatequation abstract waveequation diffusionphenomenon 1 introductionthe main objective of this work is to establish an estimate of the differencebetween the solution u of the abstract dissipative wave equationu 00 u 0 au 0 u 0 u 0 u 0 0 u 1 1 1 and the solution v of the abstract heat equationv 0 av 0 v 0 u 0 u 1 1 2 article in press corresponding author e mail address haraux ann jussieu fr a haraux 0022 0396 03 seefrontmatterr 2003 elsevierscience usa allrights reserved doi 10 1016 s0022 0396 03 00057 3

a fast sweeping method for eikonal equations in this paper a fast sweeping method for computing the numerical solution of eikonal equations on a rectangular grid is presented the method is an iterative method which uses upwind difference for discretization and uses gauss seidel iterations with alternating sweeping ordering to solve the discretized system the crucial idea is that each sweeping ordering follows a family of characteristics of the corresponding eikonal equation in a certain direction simultaneously the method has an optimal complexity of o n for n grid points and is extremely simple to implement in any number of dimensions monotonicity and stability properties of the fast sweeping algorithm are proven convergence and error estimates of the algorithm for computing the distance function is studied in detail it is shown that 2 n gauss seidel iterations is enough for the distance function in n dimensions an estimation of the number of iterations for general eikonal equations is also studied numerical examples are used to verify the analysis

identification of geometric shapes and material properties of inclusions in two dimensional finite bodies by boundary parameterization a system identification scheme based on the boundary element method bem is proposed to determine geometric shape and elastic material properties of an inclusion in a finite body the proposed algorithm is based on the minimization of least squared errors between measured displacement and calculated displacement by a boundary element model a regularization function that consists of the geometric term and material property term is added to the error function to overcome ill posedness of inverse problems to deal with the shape variation of an inclusion during the optimization process the boundary parameterization technique is applied to the bem the recursive quadratic programming rqp technique with line search is used for optimization

the lp lq estimates of solutions to one dimensional damped wave equations and their application to the compressible flow through porous media we first obtain the lp lq estimates of solutions to the cauchy problem for one dimensional damped wave equation vtt vxx vt 0 v vt t 0 v0 v1 x x t r r corresponding to that for the parabolic equation t xx 0 t 0 v0 v1 x the estimates are shown by v t e t 2v0 t v0 t 2lp ct 121q 1p 1 v0 v1 lq t 1 etc for 1 q p to show the explicit formula of the damped wave equation will be used to apply the estimates to nonlinear problems is the second aim we will treat the system of a compressible flow through porous media the solution is expected to behave as the diffusion wave which is the solution to the porous media equation due to the darcy law when the initial data has the same constant state at a sharp lp convergence rate for p 2 has been recently obtained by nishihara proc roy soc edinburgh sect a 133a 2003 1 20 by choosing a suitably located diffusion wave we will show the l1 convergence applying

finite element transport modeling using analytic element flow solutions 1 finite element methods for solute transport simulation typically use a discrete representation of the flow domain obtained from a finite element solution of the associated groundwater flow problem velocity saturated thickness and components of the dispersion coefficient tensor are represented as a set of nodal and or element averaged values in contrast the analytic element method aem provides continuous mesh independent solutions for these variables in this paper a set of techniques for using two dimensional aem flow solutions as the basis of finite element solute transport models is introduced first a general aem based discretization approach is presented that addresses the existence of curved boundaries singularities and discontinuities in vertically averaged concentration second residual integration methods that handle continuous parameters with internal and boundary singularities are developed and evaluated third an approach is introduced for handling internal discontinuities in concentration across certain analytic elements this new approach uses a nonstandard mesh topology and a new formulation for internal coupled boundary conditions the aem based transport simulation methods introduced in this paper are demonstrated to be robust and accurate for a variety of test problems

front propagation and phase field theory the connection between the weak theories for a class of geometric equations and the asymptotics of appropriately rescaled reaction diffusion equations is rigorously established two different scalings are studied in the first the limiting geometric equation is a first order equation in the second it is a generalization of the mean curvature equation intrinsic definitions for the geometric equations are obtained and uniqueness under a geometric condition on the initial surface is proved in particular in the case of the mean curvature equation this condition is satisfied by surfaces that are strictly starshaped that have positive mean curvature or that satisfy a condition that interpolates between the positive mean curvature and the starshape conditions

an explicit update scheme for inverse parameter and interface estimation of piecewise constant coefficients in linear elliptic pdes we introduce a general and efficient method to recover piecewise constant coefficients occurring in elliptic partial differential equations as well as the interface where these coefficients have jump discontinuities for this purpose we use an output least squares approach with level set and augmented lagrangian methods our formulation incorporates the inherent nature of the piecewise constant coefficients which eliminates the need for a complicated nonlinear solve at every iteration instead we obtain an explicit update formula and therefore vastly speed up computation we employ our approach to the example problems of poisson s equation and linear elasticity and provide the combination of simultaneously recovering coefficients and interface

a quadratic plane triangular element immune to quadratic mesh distortions under quadratic displacement fields abstract a quadratic plane triangular element is developed extending the concepts of us quad8 element the element belongs to the broad class of petrov galerkin formulation which is characterized by the choice of test and trial functions from different spaces the performance of the proposed element has been studied for typical static and free vibration problems the element exhibits a high degree of tolerance to mesh distortions as compared to the classical isoparametric quadratic triangular element for undistorted meshes however the performance is similar to that of the classical element

local bisection refinement for n simplicial grids generated by reflection a simple local bisection refinement algorithm for the adaptive refinement of n simplicial grids is presented the algorithm requires that the vertices of each simplex be ordered in a special way re

mesh smoothing using a posteriori error estimates we develop a simple mesh smoothing algorithm for adaptively improving finite element triangulations the algorithm makes use of a posteriori error estimates which are now widely used in finite element calculations in this paper we derive the method present some numerical illustrations and give a brief analysis of the issue of uniqueness

on the adjacencies of triangular meshes based on skeleton regular partitions for any 2d triangulation the 1 skeleton mesh of is the wireframe mesh defined by the edges of while that for any 3d triangulation the 1 skeleton and the 2 skeleton meshes respectively correspond to the wireframe mesh formed by the edges of and the surface mesh defined by the triangular faces of a skeleton regular partition of a triangle or a tetrahedra is a partition that globally applied over each element of a conforming mesh where the intersection of adjacent elements is a vertex or a common face or a common edge produce both a refined conforming mesh and refined and conforming skeleton meshes such a partition divides all the edges and all the faces of an individual element in the same number of edges faces we prove that sequences of meshes constructed by applying a skeleton regular partition over each element of the preceding mesh have an associated set of difference equations which relate the number of elements faces edges and vertices of the nth and n 1 th meshes by using these constitutive difference equations we prove that asymptotically the average number of adjacencies over these meshes number of triangles by node and number of tetrahedra by vertex is constant when n goes to infinity we relate these results with the non degeneracy properties of longest edge based partitions in 2d and include empirical results which support the conjecture that analogous results hold in 3d

a stitching method for the generation of unstructured meshes for use with co volume solution techniques abstract the successful implementation of co volume time domain solution techniques requires the use of high quality smooth dual meshes the generation of delaunay voronoi diagrams with these properties for two dimensional domains of complicated geometrical shape is considered in the adopted approach near boundary regions are discretised according to prescribed criteria and the remainder of the computational domain is discretised using an ideal mesh the two meshes are stitched together to provide a consistent mesh for the complete domain after smoothing the resulting mesh is found to be of a quality which exceeds that of meshes produced by standard automatic unstructured mesh generation methods examples involving electromagnetic wave scattering are included to demonstrate the computational performance that can be achieved with a co volume time domain solution algorithm on these meshes

nonexistence of global solutions for a time fractional damped wave equation in a k times halved space abstract in this paper we study the time fractional damped wave equation c d 0 u u c d 0 u u p t 0 x d k where 1 2 0 1 c d 0 is the left sided caputo fractional derivative of order with respect to the variable time t p 1 and d k k 1 2 n is the k times halved space given by d k x x 1 x 2 x n r n x i 0 i 1 2 k using the nonlinear capacity method we prove that the problem admits no global weak solutions with suitable initial data when 1 p 1 2 n k 2 1

mid node admissible spaces for quadratic triangular 2d finite elements with one edge curved a robust element distortion metric based on the new concept of mid node admissible spaces for two dimensional quadratic triangular finite elements is developed the metric is based on the jacobian determinant over the entire element without requiring that it actually be computed everywhere on the element the metric is relatively inexpensive to compute especially for mildly distoted elements the metric is able to detect elementsof poor quality that other distortion metrics fall to detect it also has the ability to approve elements of good quality regardless of the extent to which they may appear geometrically distorted copyright 2001 john wiley sons ltd

a close look at valences in hexahedral element meshes this paper discusses using valences in objective functions for topological modification of 3d hexahedral meshes for topological optimization of 2d quadrilateral meshes node valence i e number of element edges attached to each node is used to maximize the number of regular nodes i e nodes with four attached edges difficulties in developing 3d hexahedral local topology modifications have limited the success of hexahedral topology optimization although published literature suggests using an object function based on node valence however in this paper we show that node valence is not a consistent measure of good hexahedral element topology and objective functions based on node valence can lead to element topology which will only admit concave element shapes instead we propose that objective functions based on edge valence i e number of quadrilateral faces attached to each element edge will provide a consistent measure of element topology copyright 2010 john wiley sons ltd

automated adaptive time discontinuous finite element method for unsteady compressible airfoil aerodynamics an adaptive finite element methodology for unsteady compressible aerodynamics is presented the automated adaptive environment consists of the finite quadtree automatic mesh generator a time discontinuous galerkin least squares finite element flow solver an error indicator based on interpolation estimates and a mesh enrichment procedure specifically a linear space time wedge element formulation was developed and implemented for two dimensional problems with relative body motion the mesh enrichment procedure is developed to enable the solution process to be spatially adaptive h refinement is edge based and stores no mesh enrichment history

estimation of interfaces from boundary measurements the determination of an interface in an elliptic differential equation from dirichlet and neumann boundary data is investigated uniqueness of the function characterizing the interface is proved for numerical purposes the problem is formulated as an optimization problem involving constraints that are based on potential theory an augmented lagrangian formulation is used for the solution of the optimization problem its convergence is investigated and numerical experiments are described

asymptotic behavior of solutions of quasilinear hyperbolic equations with linear damping we consider the asymptotic behavior of the solution of quasilinear hyperbolic equation with linear dampingvtt a vx x vt 0 x t r 0 subsequent to k nishihara j differential equations131 1996 171 188 in that article the system with dampingvt ux 0 ut p v x u p v 0 was treated and the convergence rates to the diffusion wave by l hsiao and t p liu comm math phys 143 1992 599 605 and l hsiao and t p liu chinese ann math ser b14 1993 465 480 were improved for initial data v0 u0 x satisfying v0 u0 v0 0 and v0 x v0 dx 0 this system is reduced to the quasilinear hyperbolic equation with linear dampingvtt p v0 vx p v0 x vt 0 and the decay rates v t l o t 1 2 vx t l o t 1 vt t l o t 3 2 were obtained provided that v vt t 0 h3 h2 is small and inl1 l1 from these decay rates vis expected to behave as a solution to the parabolic equation the aims of this paper are to seek the asymptotic profile x t satisfying t l o t 1 2 x t l o t 1 t t l o t 3 2 and to show that the solution of satisfies v t l o t 1 v x t l o t 3 2 v t t l o t 2 the proof is based on the elementary energy method and the green function method for the parabolic equation

planar mesh refinement cannot be both local and regular we show that two desirable properties for planar mesh refinement techniques are incompatible mesh refinement is a common technique for adaptive error control in generating unstructured planar triangular meshes for piecewise polynomial representations of data local refinements are modifications of the mesh that involve a fixed maximum amount of computation independent of the number of triangles in the mesh regular meshes are meshes for which every interior vertex has degree 6 at least for some simple model meshing problems optimal meshes are known to be regular hence it would be desirable to have a refinement technique that if applied to a regular mesh produced a larger regular mesh we call such a technique a regular refinement in this paper we prove that no refinement technique can be both local and regular our results also have implications for non local refinement techniques such as delaunay insertion or rivara s refinement

on the inverse problem of identifying lame coefficients in linear elasticity an output least squares type functional is employed to identify the lame parameters in linear elasticity to be able to identify even the discontinuous lame parameters the regularization is performed by the bv seminorm finite element discretization is used and convergence analysis is given numerical examples are given to show the feasibility of the approach

structural optimization using sensitivity analysis and a level set method in the context of structural optimization we propose a new numerical method based on a combination of the classical shape derivative and of the level set method for front propagation we implement this method in two and three space dimensions for a model of linear or nonlinear elasticity we consider various objective functions with weight and perimeter constraints the shape derivative is computed by an adjoint method the cost of our numerical algorithm is moderate since the shape is captured on a fixed eulerian mesh although this method is not specifically designed for topology optimization it can easily handle topology changes however the resulting optimal shape is strongly dependent on the initial guess

mesh relaxation a new technique for improving triangulations summary given a list of points defining a domain boundary a three stage process is often used to triangulate a domain first an appropriate distribution of interior points is generated next the points are connected to form triangles and finally the connectivity data are used to reposition the interior points using the laplacian smoothing technique thereby usually improving the shapes of the triangles this paper describes a new technique for mesh improvement adjusting the connection structure during the second stage of this process the new scheme which we call mesh relaxation consists of a procedure for iteratively making the mesh topology more regular by edge swapping for each interior edge a relaxation index is computed that depends on the degrees of its end points and adjacent points any edge for which this index exceeds a prescribed threshold will be swapped i e replaced by a new edge connecting the adjacent points of the original edge after all edge swaps are completed laplacian smoothing is applied to the mesh examples show that when the mesh point density varies smoothly and due care is taken in the vicinity of the boundary mesh relaxation can dramatically increase the regularity of the mesh and produce improved triangle shapes

on the critical exponent for reaction diffusion equations in this paper we study the initial boundary value problem for u t u h t u p with homogeneous dirichlet boundary conditions where h t t q for large t let s sup s positive solutions w of u t u such that mathop lim sup limits t to infty t s parallel w cdot t parallel infty infty then for p 1 q 1 s we show if p p there are global positive solutions that decay to zero uniformly for t if 1 p p then all nontrivial solutions blow up in finite time we determine p for some conical domains in r 2 and r 3 a similar result is derived for a bounded domain if h t e t for large t

damped wave equation with a critical nonlinearity we study large time asymptotics of small solutions to the cauchy problem for nonlinear damped wave equations with a critical nonlinearity 2 t u t u u u 1 2 n 0 x r n t 0 u 0 x eu 0 x t u 0 x eu 1 x x r n where e 0 and space dimensions n 1 2 3 assume that the initial data uo h 0 n h 0 u 1 e h 1 0 n h 1 where n 2 weighted sobolev spaces are h l m e l2 m l x l 2 1 x 2 also we suppose that 2 n 0 u 0 x dx 0 where then we prove that there exists a positive e 0 such that the cauchy problem above has a unique global solution u c 0 oo h 0 satisfying the time decay property u t e g t x e t lp ce 1 2 n g 1 n 2 t n 2 1 1 p for all t 0 1 p where e 0 e 0

long time behavior of solutions to a nonlinear hyperbolic relaxation system abstract we study the large time behavior of solutions of a one dimensional hyperbolic relaxation system that may be written as a nonlinear damped wave equation first we prove the global existence of a unique solution and their decay properties for sufficiently small initial data we also show that for some large initial data solutions blow up in finite time for quadratic nonlinearities we prove that the large time behavior of solutions is given by the fundamental solution of the viscous burgers equation in some other cases the convection term is too weak and the large time behavior is given by the linear heat kernel

existence and nonexistence of time global solutions to damped wave equation on half line on the half line r 0 infinity the initial boundary value problems with null dirichlet boundary for both the semilinear heat equation and damped wave equation are considered the critical exponent p c n k of semilinear term for the existence and nonexistence about the semilinear heat equation on the halved space d n d k r k rn k is given by p c n k 1 2 n k j appl math phys 39 1988 135 149 arch rational mech anal 109 1990 63 71 since the damped wave equation is expected to be close to the heat equation j differential equations 191 2003 445 469 math z 244 2003 631 649 the critical exponent for the semilinear damped wave equation is expected to be same as that of the semilinear heat equation however there is no blow up result on the halved space for the damped wave equation in this paper the exponent pc l 1 2 is shown to be critical for the existence and nonexistence of time global solution to both the semilinear heat equation and damped wave equation on the half line r together with the derivation of the blow up time for the proof the explicit formulas of solutions are used in a similar fashion to those in li and zhou discrete continuous dynamic systems 1 1995 503 520 c 2005 elsevier ltd all rights reserved

large time behavior and lp lq estimate of solutions of 2 dimensional nonlinear damped wave equations abstract we show the asymptotic behavior of the solution to the cauchy problem of the two dimensional damped wave equation it is shown that the solution of the linear damped wave equation asymptotically decompose into a solution of the heat and wave equations and the difference of those solutions satisfies the lp lq type estimate this is a two dimensional generalization of the three dimensional result due to nishihara math z 244 2003 631 to show this we use the fourier transform and observe that the evolution operators of the damped wave equation can be approximated by the solutions of the heat and wave equations by using the lp lq estimate we also discuss the asymptotic behavior of the semilinear problem of the damped wave equation with the power nonlinearity u u our result covers the whole super critical case 1 where the 1 is well known as the fujita exponent when n 2

parameter identification for elliptic problems abstract the problem of computing a principal coefficient function p in the differential equation p x u f x r m m 1 on a bounded region from a knowledge of the solution function u and the right hand side f where u f are known only approximately and p may have mild discontinuities is solved by minimization of an associated functional

improved vector fem solutions of maxwell s equations using grid pre conditioning the time domain vector finite element method is a promising new approach for solving maxwell s equations on unstructured triangular grids this method is sensitive to the quality or condition of the grid in this study grid pre conditioning techniques such as edge swapping laplacian smoothing and energy minimization are shown to improve the accuracy of the solution and also reduce the overall computational effort 1997 john wiley sons ltd

an adaptive method for computing invariant manifolds in non autonomous three dimensional dynamical systems abstract we present a computational method for determining the geometry of a class of three dimensional invariant manifolds in non autonomous aperiodically time dependent dynamical systems the presented approach can be also applied to analyse the geometry of 3d invariant manifolds in three dimensional time dependent fluid flows the invariance property of such manifolds requires that at any fixed time they are given by surfaces in r 3 we focus on a class of manifolds whose instantaneous geometry is given by orientable surfaces embedded in r 3 the presented technique can be employed in particular to compute codimension one invariant stable and unstable manifolds of hyperbolic trajectories in 3d non autonomous dynamical systems which are crucial in the lagrangian transport analysis the same approach can also be used to determine evolution of an orientable material surface in a fluid flow these developments represent the first step towards a non trivial 3d extension of the so called lobe dynamics a geometric invariant manifold based framework which has been very successful in the analysis of lagrangian transport in unsteady two dimensional fluid flows in the developed algorithm the instantaneous geometry of an invariant manifold is represented by an adaptively evolving triangular mesh with piecewise c 2 interpolating functions the method employs an automatic mesh refinement which is coupled with adaptive vertex redistribution a variant of the advancing front technique is used for remeshing whenever necessary such an approach allows for computationally efficient determination of highly convoluted evolving geometry of codimension one invariant manifolds in unsteady three dimensional flows we show that the developed method is capable of providing detailed information on the evolving lagrangian flow structure in three dimensions over long periods of time which is crucial for a meaningful 3d transport analysis

lp lq estimates of solutions to the damped wave equation in 3 dimensional space and their application it has been asserted that the damped wave equation has the diffusive structure as t in this paper we consider the cauchy problem in 3 dimensional space for the linear damped wave equation and the corresponding parabolic equation and obtain the lp lq estimates of the difference of each solution which represent the assertion precisely explicit formulas of the solutions are analyzed for the proof the second aim is to apply the lp lq estimates to the semilinear damped wave equation with power nonlinearity if the power is larger than the fujita exponent then the time global existence of small weak solution is proved and its optimal decay order is obtained

sequential and parallel splitting methods for bilinear control problems in hilbert spaces an augmented lagrangian method with second order update is developed and its relationship to the sequential quadratic programming method is described the rate of convergence proof depends on a second order sufficient optimality condition which is shown to be satisfied for a class of nonlinear optimal control problems of tracking type numerical examples are included which demonstrate the globalizing effect of the augmented lagrangian method

an approach to the generation of triangular grids possessing few obtuse triangles a triangular mesh generator is presented which makes extensive use of side swapping and mesh smoothing to create a grid with few obtuse triangles to perform the above task a data structure is presented which holds full adjacency information both for nodes and elements it is shown how this data structure is employed in the process mesh generation and how the methods of computational geometry such as region decomposition are used not only to decompose a complex region but also to reflect the boundary grading into the interior the region algorithms are provided to show the mechanism of these processes and practical examples are given to support the approach

structural boundary design via level set and immersed interface methods we develop and test an algorithmic approach to the boundary design of elastic structures the goal of our approach is two fold first to develop a method which allows one to rapidly solve the two dimensional lam equations in arbitrary domains and compute for example the stresses and second to develop a systematic way of modifying the design to optimize chosen properties at the core our approach relies on two distinct steps given a design we first apply an explicit jump immersed interface method to compute the stresses for a given design shape we then use a narrow band level set method to perturb this shape and progress towards an improved design the equations of 2d linear elastostatics in the displacement formulation on arbitrary domains are solved quickly by domain embedding and the use of fast elastostatic solvers this effectively reduces the dimensionality of the problem by one once the stresses are found the level set method which represents the design structure through an embedded implicit function is used in the second step to alter the shape with velocities depending on the stresses in the current design criteria are provided for advancing the shape in an appropriate direction and for correcting the evolving shape when given constraints are violated

decay properties of solutions to the cauchy problem for the damped wave equation with absorption abstract we consider the cauchy problem for the damped wave equation with absorption u t t u u t u p 1 u 0 t x r r n the behavior of u as t is expected to be the same as that for the corresponding heat equation t p 1 0 t x r r n which has the similarity solution w a t x with the form t 1 p 1 f x t depending on a lim x x 2 p 1 f x 0 provided that p is less than the fujita exponent p c n 1 2 n in this paper as a first step if 1 p p c n and the data u 0 u 1 x decays exponentially as x without smallness condition the solution is shown to decay with rates as t u t l 2 u t l p 1 u t l 2 o t 1 p 1 n 4 t 1 p 1 n 2 p 1 t 1 p 1 1 2 n 4 those of which seem to be reasonable because the similarity solution w a t x has the same decay rates as for the proof the weighted l 2 energy method will be employed with suitable weight similar to that in todorova and yordanov y todorova b yordanov critical exponent for a nonlinear wave equation with damping j differential equations 174 2001 464 489

electrical impedance tomography using level set representation and total variational regularization in this paper we propose a numerical scheme for the identification of piecewise constant conductivity coefficient for a problem arising from electrical impedance tomography the key feature of the scheme is the use of level set method for the representation of interface between domains with different values of coefficients numerical tests show that our method can recover sharp interfaces and can tolerate a relatively high level of noise in the observation data results concerning the effects of number of measurements noise level in the data as well as the regularization parameters on the accuracy of the scheme are also given

robust boundary triangulation and delaunay triangulation of arbitrary planar domains a simple and robust boundary triangulation algorithm is proposed and based on it completely automatic delaunay mesh generation procedures are developed the algorithm is equally applicable to convex non convex and multiply connected planar domains in this approach given the nodes the number of triangles formed is precisely known and any desired control over mesh generation is possible