Parametric Analysis Of ACA-based Solver For BEM 3D
Author(s)
T. Grytsenko & A. Peratta
Abstract
Parametric analysis of ACA-based solver for
BEM 3D
T. Grytsenko & A. Peratta
Wessex Institute of Technology, UK
Abstract
The standard Boundary Element Method (BEM) with single domain yields the
dense linear system of equation (LSE). This LSE cannot be solved efficiently by
existing iterative solvers such as CG, GMRES, TFQMR, etc. Moreover, such
LSE cannot be stored in advanced formats such as Compressed Sparse Row or
Modified Sparse Row and therefore cannot be compressed in order to economise
memory consumption. Methods such as the fast multipole method and panel
clustering gain their efficiency from approximating the kernel function. This
paper implements and studies the parameters and performance of the Adaptive
Cross Approximation (ACA) algorithm for reducing the rank of off-diagonal
blocks in the three dimensional BEM. The ACA algorithm is purely algebraic
and does not need to deal with the kernel. The algorithm uses a hierarchical
matrix storage approach where the matrix is split into many blocks. The
off-diagonal blocks of this matrix represent remote interactions between source
points and are therefore approximated by low-rank matrices with the ACA
approach. Those blocks, which describe close interactions between source
points, are stored without any changes. These reorganisations in conjunction
with novel algorithms for manipulation with H-matrices reduce the calculation
complexity of matrix-vector multiplication (MVM) to approximately ) (N O .
This simplification of MVM paves the road for speeding up of the solution of
LSE coming from BEM, as MVM is a key-operation for many existing solvers.
This paper analyses the ACA-based solver and describes how to choose
parameters for this solver when used in conjunction with BEM. Finally, a 3D
numerical example solved with this technique is presented.
Keywords: BEM 3D, hierarchical matrix, adaptive cross approximation,
iterative solver.
Keywords
BEM 3D, hierarchical matrix, adaptive cross approximation,
iterative solver.
Related Book
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