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Sweeping Preconditioner for the Helmholtz Equation:Hierarchical Matrix Representation
Sweeping Preconditioner Helmholtz Equation Hierarchical Matrix Representation
2015/7/14
The paper introduces the sweeping preconditioner, which is highly efficient for iterative solutions of the variable-coefficient Helmholtz equation including veryhigh-frequency problems. The first cent...
SWEEPING PRECONDITIONER FOR THE HELMHOLTZ EQUATION: MOVING PERFECTLY MATCHED LAYERS
Helmholtz equation perfectly matched layers high frequency waves preconditioners LDLt factorization Green’s function multifrontal methods optimal ordering
2015/7/14
This paper introduces a new sweeping preconditioner for the iterative solution of the variable coefficient Helmholtz equation in two and three dimensions. The algorithms follow the general structure o...
A sweeping preconditioner for Yee’s finite difference approximation of time-harmonic Maxwell’s equations
Electromagnetic scattering Yee grid finite difference methods perfectly matched layers LDLT factorizations multifrontal method wave propagation in inhomogeneous and anisotropic media matrix preconditioners
2015/7/14
This paper is concerned with the fast iterative solution of linear systems arising from finite difference discretizations in electromagnetics. The sweeping preconditioner with moving perfectly matched...
A sweeping preconditioner for time-harmonic Maxwell’s equations with finite elements
Maxwell’s equations Frequency domain Finite element methods Preconditioners Fast solvers Perfectly matched layers Block LDLt factorization High-frequency waves
2015/7/14
This paper is concerned with preconditioning the stiffness matrix resulting from finite element discretizations of Maxwell’s equations in the high frequency regime. The moving PML sweeping preconditio...
A PARALLEL SWEEPING PRECONDITIONER FOR HETEROGENEOUS 3D HELMHOLTZ EQUATIONS
Helmholtz time-harmonic sweeping preconditioner parallel
2015/7/14
A parallelization of a sweeping preconditioner for 3D Helmholtz equations without internal resonance is introduced and benchmarked for several challenging velocity models. The setup and application co...
SPARSIFYING PRECONDITIONER FOR PSEUDOSPECTRAL APPROXIMATIONS OF INDEFINITE SYSTEMS ON PERIODIC STRUCTURES
Helmholtz equation Schrodinger equation preconditioner pseudospectral approximation indefinite matrix periodic structure sparse linear algebra
2015/7/14
This paper introduces the sparsifying preconditioner for the pseudospectral approximation of highly indefinite systems on periodic structures, which include the frequency-domain response problems of t...
SPARSIFYING PRECONDITIONER FOR THE LIPPMANN–SCHWINGER EQUATION
Lippmann–Schwinger equation acoustic and electromagnetic scattering quantum scattering preconditioner sparse linear algebra
2015/7/14
The Lippmann–Schwinger equation is an integral equation formulation for acoustic and electromagnetic scattering from an inhomogeneous medium and quantum scattering from a localized potential. We prese...
DIRECTIONAL PRECONDITIONER FOR HIGH FREQUENCY OBSTACLE SCATTERING
Boundary integral method scattering high-frequency waves preconditioner low-rank approximation sparse linear algebra
2015/7/14
The boundary integral method is an efficient approach for solving time-harmonic obstacle scattering problems by a bounded scatterer. This paper presents the directional preconditioner for the iterativ...
Additive Sweeping Preconditioner for the Helmholtz Equation
Helmholtz equation perfectly matched layers preconditioners high frequency waves
2015/7/14
We introduce a new additive sweeping preconditioner for the Helmholtz equation based on the perfect matched layer (PML). This method divides the domain of interest into thin layers and proposes a new ...
Recursive Sweeping Preconditioner for the 3D Helmholtz Equation
Helmholtz equation perfectly matched layers preconditioners high frequency waves
2015/7/14
This paper introduces the recursive sweeping preconditioner for the numerical solution of the Helmholtz equation in 3D. This is based on the earlier work of the sweeping preconditioner with the moving...
A New Preconditioner with Two Variable Relaxation Parameters for Saddle Point Linear Systems with Highly Singular(1,1) Blocks
Saddle Point Linear Systems Block Triangular Preconditioner Krylov Subspace Methods
2013/1/30
In this paper, we provide new preconditioner for saddle point linear systems with (1,1) blocks that have a high nullity. The preconditioner is block triangular diagonal with two variable relaxation pa...
Multigrid Preconditioner for Nonconforming Discretization of Elliptic Problems with Jump Coefficients
Multigrid Preconditioner Elliptic Problems Jump Coefficients Numerical Analysis
2011/9/1
Abstract: In this paper, we present a multigrid preconditioner for solving the linear system arising from the piecewise linear nonconforming Crouzeix-Raviart discretization of second order elliptic pr...
Computing an approximate inverse preconditioner by successive approximations method
Successive approximations method Sylvester equation
2010/9/17
A method for computing an approximate inverse preconditioner of a matrix A which all eigenvalues have negative real parts is proposed. The approximate solution of the special Sylvester matrix equation...
An Efficient Preconditioner for Iterative Solvers
Method of Moments iterative solution LU factorization
2009/7/28
The method of moments solution of the Maxwell's equations leads to a dense system of complex equations. Direct solution of these equations using LU factorization becomes unwieldy as the size of the sc...
A SHIFT-SPLITTING PRECONDITIONER FOR NON-HERMITIAN POSITIVE DEFINITE MATRICES
Non-Hermitian positive definite matrix Matrix splitting Preconditioning Krylov subspace method Convergence
2007/12/12
A shift splitting concept is introduced and, correspondingly,
a shift-splitting iteration scheme and a shift-splitting
preconditioner are presented,
for solving the large sparse system of linear eq...