TY - JOUR

T1 - Parallel adaptive solution of a Poisson equation with multiwavelets

AU - Averbuch, A.

AU - Braverman, E.

AU - Israeli, M.

PY - 2001

Y1 - 2001

N2 - We present an adaptive algorithm for the solution of the Poisson equation. The domain is divided into subdomains. The resolution of each subdomain depends on the smoothness of the right-hand side of the Poisson equation. This determines the adaptivity of the algorithm. In each subdomain a particular solution is found. These solutions are patched by introducing double/single layers at the interfaces of the subdomains. The influence of these layers is effectively computed using multiwavelets. In the wavelet bases kernels of integrals which represent double layers are sparse. When the number of grid points increases as N, the number of essential wavelet coefficients, which represent a vector, increases as log N. Hence, using this sparsity reduces the number of operations from O(N2) to O(N log N). The algorithm was implemented on parallel computers of SP2 and SGI types while each processor was assigned to each box. The efficiency of the algorithm was demonstrated.

AB - We present an adaptive algorithm for the solution of the Poisson equation. The domain is divided into subdomains. The resolution of each subdomain depends on the smoothness of the right-hand side of the Poisson equation. This determines the adaptivity of the algorithm. In each subdomain a particular solution is found. These solutions are patched by introducing double/single layers at the interfaces of the subdomains. The influence of these layers is effectively computed using multiwavelets. In the wavelet bases kernels of integrals which represent double layers are sparse. When the number of grid points increases as N, the number of essential wavelet coefficients, which represent a vector, increases as log N. Hence, using this sparsity reduces the number of operations from O(N2) to O(N log N). The algorithm was implemented on parallel computers of SP2 and SGI types while each processor was assigned to each box. The efficiency of the algorithm was demonstrated.

KW - Adaptive algorithms

KW - Double and single layers

KW - Multiwavelet bases

KW - Sparse data structures

UR - http://www.scopus.com/inward/record.url?scp=0034973446&partnerID=8YFLogxK

U2 - 10.1137/S106482759833694X

DO - 10.1137/S106482759833694X

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AN - SCOPUS:0034973446

VL - 22

SP - 1053

EP - 1086

JO - SIAM Journal of Scientific Computing

JF - SIAM Journal of Scientific Computing

SN - 1064-8275

IS - 3

ER -