A fast numerical algorithm is proposed for calculating the difference field radar cross-section of an object above a rough surface. The electric-field integral equation of the difference of the induced current on the ...
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A fast numerical algorithm is proposed for calculating the difference field radar cross-section of an object above a rough surface. The electric-field integral equation of the difference of the induced current on the rough surface and the induced current on the object is derived, which is solved by an iterative solver. The characteristic basis functions are used to calculate the induced current on the rough surface, which is part of the right-hand side of the system. It is observed that the coupling matrices (nonself-block interactions of the rough surface and the interactions between the object and the rough surface) are rank deficient. The matrix decomposition algorithm is used and extended to compress the coupling matrices. Numerical examples show that the characteristic basis functions method combined with the matrix decomposition algorithm can greatly reduce the CPU time and memory cost. The accuracy and efficiency are discussed by numerical examples.
We propose efficient fast Fourier transform (FFT)-based algorithms using the method of fundamental solutions (MFS) for the numerical solution of certain problems in planar thermoelasticity. In particular, we consider ...
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We propose efficient fast Fourier transform (FFT)-based algorithms using the method of fundamental solutions (MFS) for the numerical solution of certain problems in planar thermoelasticity. In particular, we consider problems in domains possessing radial symmetry, namely disks and annuli and it is shown that the MFS matrices arising in such problems possess circulant or block-circulant structures. The solution of the resulting systems is facilitated by appropriately diagonalizing these matrices using FFTs. Numerical experiments demonstrating the applicability of these algorithms are also presented.
We formulate a fourth order modified nodal cubic spline collocation scheme for variable coefficient second order partial differential equations in the unit cube subject to nonzero Dirichlet boundary conditions. The ap...
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We formulate a fourth order modified nodal cubic spline collocation scheme for variable coefficient second order partial differential equations in the unit cube subject to nonzero Dirichlet boundary conditions. The approximate solution satisfies a perturbed partial differential equation at the interior nodes of a uniform partition of the cube and the partial differential equation at the boundary nodes. In the special case of Poisson's equation, the resulting linear system is solved by a matrix decomposition algorithm with fast Fourier transforms at a cost . For the general variable coefficient diffusion-dominated case, the system is solved using the preconditioned biconjugate gradient stabilized method.
matrix decomposition algorithms (MDAs) employing fast Fourier transforms are developed for the solution of the systems of linear algebraic equations arising when the finite element Galerkin method with piecewise Hermi...
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matrix decomposition algorithms (MDAs) employing fast Fourier transforms are developed for the solution of the systems of linear algebraic equations arising when the finite element Galerkin method with piecewise Hermite bicubics is used to solve Poisson's equation on the unit square. Like their orthogonal spline collocation counterparts, these MDAs, which require O(N (2)logN) operations on an NxN uniform partition, are based on knowledge of the solution of a generalized eigenvalue problem associated with the corresponding discretization of a two-point boundary value problem. The eigenvalues and eigenfunctions are determined for various choices of boundary conditions, and numerical results are presented to demonstrate the efficacy of the MDAs.
We propose an efficient matrixdecomposition Method of Fundamental Solutions algorithm for the solution of certain two-dimensional linear elasticity problems. In particular, we consider the solution of the Cauchy-Navi...
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We propose an efficient matrixdecomposition Method of Fundamental Solutions algorithm for the solution of certain two-dimensional linear elasticity problems. In particular, we consider the solution of the Cauchy-Navier equations in circular domains subject to Dirichlet boundary conditions, that is when the displacements are prescribed on the boundary. The proposed algorithm is extended to the case of annular domains. Numerical experiments for both types of problems are presented.
The method of fundamental solutions is a boundary-type meshless method for the solution of certain elliptic boundary value problems. By exploiting the structure of the matrices appearing when this method is applied to...
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The method of fundamental solutions is a boundary-type meshless method for the solution of certain elliptic boundary value problems. By exploiting the structure of the matrices appearing when this method is applied to certain three-dimensional potential problems, we develop an efficient matrix decomposition algorithm for their solution. (C) 2003 Elsevier Ltd. All rights reserved.
We study the computation of the orthogonal spline collocation solution of a linear Dirichlet boundary value problem with a nonselfadjoint or an indefinite operator of the form Lu = Sigmaa(ij) (x) u(xixj) + Sigma b(i)(...
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We study the computation of the orthogonal spline collocation solution of a linear Dirichlet boundary value problem with a nonselfadjoint or an indefinite operator of the form Lu = Sigmaa(ij) (x) u(xixj) + Sigma b(i)(x) u(xi) + c(x) u. We apply a preconditioned conjugate gradient method to the normal system of collocation equations with a preconditioner associated with a separable operator, and prove that the resulting algorithm has a convergence rate independent of the partition step size. We solve a problem with the preconditioner using an efficient direct matrix decomposition algorithm. On a uniform N x N partition, the cost of the algorithm for computing the collocation solution within a tolerance epsilon is O(N-2 lnN| ln epsilon|).
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