fast multipole method for scattering from an arbitrary pec target above or buried in a lossy half space the fast multipole method fmm was originally developed for perfect electric conductors pecs in free space through exploitation of the spectral properties of the free space green s function in the work reported here the fmm is modified for scattering from an arbitrary three dimensional 3 d pec target above or buried in a lossy half space the near terms in the fmm are handled via the original method of moments mom analysis wherein the half space green s function is evaluated efficiently and rigorously through application of the method of complex images the far fmm interactions which employ a clustering of expansion and testing functions utilize an approximation to the green s function dyadic via real image sources and far field reflection dyadics the half space fmm algorithm is validated through comparison with results computed via a rigorous mom analysis further a detailed comparison is performed on the memory and computational requirements of the mom and fmm algorithms for a target in the vicinity of a half space interface

some convergence estimates for semidiscrete type schemes for time dependent nonselfadjoint parabolic equations l2 norm error estimates are shown for semidiscrete continuous in time galerkin finite element type approximations to solutions of general time dependent nonselfadjoint second order parabolic equations under dirichlet boundary conditions the semidiscrete solutions are defined in terms of given methods for the corresponding elliptic problem such as the standard galerkin method in which the boundary conditions are satisfied exactly but also methods for which this is not necessary the results are proved by energy arguments and include estimates for the homogeneous equation with both smooth and nonsmooth initial data

boundary integral equation method for linear porous elasticity with applications to soil consolidation for physical phenomena governed by the biot model of porous elasticity a reciprocal relation similar to the betti s recoprocal theorem in elasticity is constructed in laplace transformed space integrating the reciprocal relation enables one to formulate boundary integral equations the fundamental kernels for the integral equations are solved in closed forms for the case of isotropic material numerical implementation of two dimensional problems includes finite element ideas of discretization and polynomial interpolation and numerical inversion of a laplace transform practical applications of the method are found in consolidation problems in soils which contain compressible as well as incompressible pore fluids also as a numerical experiment consolidation of partially saturated soil is simulated and interesting phenomena are observed the currently developed boundary integral equation method biem for porous elasticity may be viewed as an efficient and accurate alternative of existing finite element and finite difference methods for linear consolidation problems application of biem is always preferred to the other numerical methods whenever possible

multilayered leaky aquifer systems 2 boundary element solutions the boundary element algorithm for the multilayered leaky aquifer system of neuman witherspoon and herrera is presented by applying the laplace transform to the integrodifferential equations of herrera a set of coupled two dimensional elliptic equations results the boundary integral representation is derived from green s theorem green s functions governed by an adjoint system of the original governing equations are found from the pumping well solutions given in part 1 by a coefficient exchange the resultant numerical system requires a discretization only at the boundaries of the planar aquifers and is free from aquitard unknowns several numerical examples including one dimensional flow pumping well problems and two dimensional problems are provided for the purpose of validation and demonstration

adaptive time stepping for incompressible flow part i scalar advection diffusion even the simplest advection diffusion problems can exhibit multiple time scales this means that robust variable step time integrators are a prerequisite if such problems are to be efficiently solved computationally the performance of the second order trapezoid rule using an explicit adams bashforth method for error control is assessed in this work this combination is particularly well suited to long time integration of advection dominated problems herein it is shown that a stabilized implementation of the trapezoid rule leads to a very effective integrator in other situations specifically diffusion problems with rough initial data and general advection diffusion problems with different physical time scales governing the system evolution

boundary integral equation solution of moving boundary phase change problems boundary integral equation methods are presented for the solution of some two dimensional phase change problems convection may enter through boundary conditions but cannot be considered within phase boundaries a general formulation based on space time green s functions is developed using the complete heat equation followed by a simpler formulation using the laplace equation the latter is pursued and applied in detail an elementary noniterative system is constructed featuring linear interpolation over elements on a polygonal boundary nodal values of the temperature gradient normal to a phase change boundary are produced directly in the numerical solution the system performs well against basic analytical solutions using these values in the interphase jump condition with the simplest formulation of the surface normal at boundary vertices because the discretized surface changes automatically to fit the scale of the problem the method appears to offer many of the advantages of moving mesh finite element methods however it only requires the manipulation of a surface mesh and solution for surface variables in some applications coarse meshes and very large time steps may be used relative to those which would be required by fixed grid domain methods computations are also compared to original lab data describing two dimensional soil freezing with a time dependent boundary condition agreement between simulated and measured histories is good

a partitioning technique for the finite element solution of electromagnetic scattering from electrically large dielectric cylinders a finite element partitioning scheme has been developed to reduce the computational costs of modeling electrically large geometries in the partitioning scheme the cylinder is divided into many sections the finite element method is applied to each section independent of the other sections and then the solutions in each section are coupled through the use of the tangential field continuity conditions between adjacent sections since the coupling matrix is significantly smaller than the original finite element matrix it is expected that both the cpu time and memory costs can be significantly reduced the partitioning scheme is coupled to the bymoment method to account for the boundary truncation numerical results are presented to demonstrate the efficiency and accuracy of the method

non smooth initial data error estimates with the weight norms for the linear finite element method of parabolic partial differential equations we analyze the galerkin approximation of a parabolic equation for the second order continuous time method with initial data only in l2 we prove an optimal order error estimate with weight norm our analysis uses elementary energy techniques and spectral representations and weight function techniques the same techniques are shown to give an analysis of the galerkin method time discretization

spectral tau approximation of the two dimensional stokes problem we analyse the spectral tau method for the approximation of the stokes system on a square with dirichlet boundary conditions we provide an error estimate in the norm of the sobolev spaceh s for the approximation of a divergence free vector field with polynomial divergence free vector fields we apply this result to prove some convergence estimates for the solution of the discrete stokes problem

finite element solution to electromagnetic scattering problems by means of the robin boundary condition iteration method a new numerical method called the robin boundary condition iteration rbci is proposed for the finite element fe solution of electromagnetic scattering problems in open boundary domains the unbounded domain is truncated to a bounded one by means of a fictitious boundary that contains the scatterer and on which a suitable nonhomogeneous robin mixed boundary condition is assumed for the helmholtz equation in the bounded domain the robin condition is expressed by means of an integral formula the second green identity in terms of the field in the interior of the bounded domain with the integration surface being a surface strictly enclosed by the truncation boundary the discretized differential and integral equations are then coupled together to solve the problem the formulation is completely immune from the well known interior resonance problems a simple and effective iterative solving scheme is described examples are also provided to validate rbci and compare it with other methods

an fem approach with fft accelerated iterative robin boundary condition for electromagnetic scattering of a target with strong or weak coupled underlying randomly rough surface to study electromagnetic scattering of a target above randomly rough surface the robin boundary condition robin bc is employed to separate and enclose two isolate regions of the target and underlying surface the fields in these two enclosed regions are strongly or weakly coupled by iteratively solving the scattering field integral equation in the finite element method fem with updating the right hand side residual of the robin bc this fem approach presents an effective calculation for the model of the target at high altitude above large scale rough surface to show their coupling interactions most time consuming of the algorithm is spent on evaluating the robin bc on the fictitious planar boundary over the large scale rough surface the scattering field integral equation is written as the one dimensional convolution form and is solved efficiently by using the fast fourier transform fft our approach is first validated by available fem ddm domain decomposition method results then the functional dependence of bistatic and back scattering from the target above rough oceanic surface upon the target altitude incident and scattering angle etc are numerically simulated and discussed this study presents a numerical description for the scattering mechanism associated with strong or weak coupled interactions of a volumetric target at various altitudes above randomly rough surface

error estimates for discontinuous galerkin approximations of implicit parabolic equations we analyze the classical discontinuous galerkin method for implicit parabolic equations symmetric error estimates for schemes of arbitrary order are presented the ideas developed allow certain assumptions frequently required in previous work to be relaxed for example different discrete spaces are allowed at each time step and the spatial operator is not required to be self adjoint or independent of time error estimates are posed in terms of projections of the exact solution onto the discrete spaces and are valid under the minimal regularity guaranteed by the natural energy estimate these projections are local and enjoy optimal approximation properties when the solution is sufficiently regular

evaluation of 2 d green s boundary formula and its normal derivative using legendre polynomials with an application to acoustic scattering problems this paper presents the non singular forms in a global sense of two dimensional green s boundary formula and its normal derivative the main advantage of the modified formulations is that they are amenable to solution by directly applying standard quadrature formulas over the entire integration domain that is the proposed element free method requires only nodal data the approach includes expressing the unknown function as a truncated fourier legendre series together with transforming the integration interval a b to 1 1 the series coefficients are thus to be determined the hypersingular integral interpreted in the hadamard finite part sense and some weakly singular integrals can be evaluated analytically the remaining integrals are regular with the limiting values of the integrands defined explicitly when a source point coincides with a field point the effectiveness of the modified formulations is examined by an elliptic cylinder subject to prescribed boundary conditions the regularization is further applied to acoustic scattering problems the well known burton miller method using a linear combination of the surface helmholtz integral equation and its normal derivative is adopted to overcome the non uniqueness problem a general non singular form of the composite equation is derived comparisons with analytical solutions for acoustically soft and hard circular cylinders are made copyright 2001 john wiley sons ltd

finite element approximation of the nonstationary navier stokes problem i regularity of solutions and second order error estimates for spatial discretization this is the first part of a work dealing with the rigorous error analysis of finite element solutions of the nonstationary navier stokes equations second order error estimates are proven for spatial discretization using conforming or nonconforming elements the results indicate a fluid like behavior of the approximations even in the case of large data so long as the solution remains regular the analysis is based on sharp a priori estimates for the solution particularly reflecting its behavior as t to 0 and as t to infty it is shown that the regularity customarily assumed in the error analysis for corresponding parabolic problems cannot be realistically assumed in the case of the navier stokes equations as it depends on nonlocal compatibility conditions for the data the results which are presented here are independent of such compatibility conditions which cannot be verified in practice

the validity of the perturbation approximation for rough surface scattering using a gaussian roughness spectrum the validity of the perturbation approximation for rough surface scattering is examined 1 by comparison with exact results obtained by solving an integral equation and 2 through comparison of low order perturbation predictions with higher order predictions the pressure release boundary condition is assumed and the field quantity calculated is the bistatic scattering cross section a gaussian roughness spectrum is used and the surfaces have height variations in only one direction it is found in general that the condition kh 1 k is the acoustic wavenumber h is the rms surface height is insufficient to guarantee the accuracy of first order or higher order perturbation theory when the surface correlation length l becomes too large or too small with h held fixed higher order perturbation terms can make larger contributions to the scattering cross section than lower order terms an explanation for this result is given the regions of validity for low order perturbation theory are also given th

saltwater intrusion in aquifers development and testing of a three dimensional finite element model a three dimensional finite element model is developed for the simulation of saltwater intrusion in single and multiple coastal aquifer systems with either a confined or phreatic top aquifer the model formulation is based on two governing equations one for fluid flow and the other for salt transport density coupling of these equations is accounted for and handled using a picard sequential solution algorithm with special provisions to enhance convergence of the iterative solution flexibility in the formulation allows for either three dimensional simulations or quasi three dimensional simulations where flow and transport in aquitards are treated using one dimensional analytical and or numerical approximations spatial discretization of three dimensional regions is performed using a vertical slicing approach designed to accommodate complex geometry with irregular boundaries layering and or lateral discontinuity this approach is effectively combined with the use of simple linear elements such as rectangular and triangular prisms and composite hexahedra and pentahedra made up of tetrahedra for these elements computation of element matrices can be performed efficiently using influence coefficient formulas that avoid numerical integration new transport influence coefficient formulas are presented for rectangular and triangular prism elements matrix assembly is performed slice by slice and the matrix solution is achieved using a slice successive relaxation scheme this permits a fairly large number of nodal unknowns of the order of five to ten thousand to be handled conveniently on small or medium size minicomputers flexibility of the formulation and matrix handling procedures also allows two dimensional and axisymmetric problems to be solved efficiently using single slice representations four examples are presented to demonstrate the model verification and utility these problems represent a fair range of physical conditions where possible simulation results are compared with previously published solutions

complex variable boundary element method for potential flow with thin objects a complex variable boundary element method cvbem is developed for potential flow in the presence of thin objects singularities caused by such objects are expressed analytically through the conformal mapping technique and the resultant singular solution is coupled with the cvbem by the principle of superposition this can be done by virtue of the semi analytic nature of the cvbem the numerical results for example problems including flow barriers and high conductivity fractures confirm that the proposed model yields accurate solutions of the velocity potential and the stream function within the flow domain

boundary element solution for stochastic groundwater flow temporal weakly stationary problems this paper continues the development of boundary integral equation technique for solving stochastic groundwater flow problems the case of aquifers under deterministic hydraulic conductivity but subject to random boundary condition and domain recharge has been investigated in an earlier paper under the assumption of steady state governing equation in the current paper the governing equation is transient but the temporal variation of second order statistical moments is assumed to be weakly stationary several examples of fundamental importance to the understanding of stochastic process are examined both by the analytical and by the numerical boundary element techniques

solving nonlinear parabolic problems with result verification part i one space dimensional case abstract we propose some numerical methods for the automatic proof of existence of weak solutions for parabolic initial boundary value problems with one space dimension it also means that one can obtain a posteriori error bounds for the approximate solutions of the problems based upon schauder s fixed point theorem a verification condition is formulated and by the use of finite element approximation and its error estimates for a simple parabolic problem we present a numerical verification algorithm of exact solutions in a computer some numerical examples which are verified by the method are illustrated

error estimates for the spectral approximation of the nonstationary stokes problem this paper analyzes a discretization of the nonstationary stokes problem with periodic nonperiodic boundary conditions fourier legendre spectral approximations are considered with respect to the space variables while the time discretization is based on the second order crank nicolson scheme optimal convergence estimates are proved for the velocity field

on the smoothing property of the galerkin method for parabolic equations we analyze the galerkin approximation of the general second order parabolic initial boundary value problem for the second order continuous time method with initial data only in l 2 we prove an l 2 error estimate of order o h 2 t analogous results are shown to hold for the error in negative sobolev norms and for the time derivative of the error our analysis uses only elementary energy techniques and the same techniques are shown to give a simple analysis of the backward euler time discretization

boundary integral equation solutions to moving interface between two fluids in porous media the boundary integral equation method is formulated for and applied to problems concerning a moving interface between two fluids in porous media the mixing between two fluids is assumed to be insignificant a sharp interface exists between them numerical and experimental results are presented for the tilting of a vertical interface in a hele shaw cell during the initial stage of the interfacial movement nonlinear effects are clearly demonstrated the biem results are also compared to experimental results for a transient salt water intrusion problem

spectral approximation of the periodic nonperiodic navier stokes equations in order to approximate the navier stokes equations with periodic boundary conditions in two directions and a no slip boundary condition in the third direction by spectral methods we justify by theoretical arguments an appropriate choice of discrete spaces for the velocity and the pressure the compatibility between these two spaces is checked via an infsup condition we analyze a spectral and a collocation pseudo spectral method for the stokes problem and a collocation pseudo spectral method for the navier stokes equations we derive error bounds of spectral type i e which behave likem wherem depends on the number of degrees of freedom of the method and represents the regularity of the data