Two-Level Block Decompositions for Solving Helmholtz Equation via Chebyshev Pseudo Spectral Method

Collection:
Clark Atlanta University Faculty Publications
Title:
Two-Level Block Decompositions for Solving Helmholtz Equation via Chebyshev Pseudo Spectral Method
Creator:
Hsin-Chu, Chen
Date of Original:
2018-09
Subject:
African Americans--Education (Higher)--Georgia
Clark Atlanta University
Location:
United States, Georgia, Fulton County, Atlanta, 33.749, -84.38798
Medium:
articles
Type:
Text
Format:
application/pdf
Description:
Abstract: In this paper, we consider solving the Helmholtz equation in the Cartesian domain , subject to homogeneous Dirichlet boundary condition, discretized with the Chebyshev pseudo-spectral method. The main purpose of this paper is to present the formulation of a two-level decomposition scheme for decoupling the linear system obtained from the discretization into independent subsystems. This scheme takes advantage of the homogeneity property of the physical problem along one direction to reduce a 2D problem to several 1D problems via a block diagonalization approach and the reflexivity property along the second direction to decompose each of the 1D problems to two independent subproblems using a reflexive decomposition, effectively doubling the number of subproblems. Based on the special structure of the coefficient matrix of the linear system derived from the discretization and a reflexivity property of the second-order Chebyshev differentiation matrix, we show that the decomposed submatrices exhibits a similar property, enabling the system to be decomposed using reflexive decompositions. Explicit forms of the decomposed submatrices are derived. The decomposition not only yields more efficient algorithm but introduces coarse-grain parallelism. Furthermore, it preserves all eigenvalues of the original matrix.
Source: Journal of Modern Physics
DOI: https://doi.org/10.4236/jmp.2018.99107
Metadata URL:
http://hdl.handle.net/20.500.12322/cau.ir:2018_hsin_chu_chen_1
Language:
eng
Original Collection:
Clark Atlanta University Faculty Publications
Holding Institution:
Clark Atlanta University
Rights:

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