Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2015, Vol. 32 ›› Issue (5): 726-742.doi: 10.3969/j.issn.1005-3085.2015.05.011

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A Fast Propagation Method for the Helmholtz Equation

LENG Wei   

  1. State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences, Beijing 100190
  • Received:2015-01-01 Accepted:2015-08-25 Online:2015-10-15 Published:2015-12-15
  • Supported by:
    The National 863 Project of China (2012AA01A309).

Abstract:

A fast method is proposed for solving the high frequency Helmholtz equation. The building block of the new fast method is an overlapping domain decomposition method for layered medium. In the new fast method, the computation domain is firstly decomposed hierarchically into many subdomains on different levels. Then the mapping from incident waves to out-going waves on all the subdomains are set up. Finally, the wave propagates on the subdomain boundaries on different levels to reach the solution to the Helmholtz equation. The new fast method is of low complexity, and suitable for parallel computing. Numerical experiments show that with the new fast method, 2D Helmholtz equations with half billion unknowns could be solved efficiently on massively parallel machines.

Key words: Helmholtz equation, finite difference, fast method, domain decomposition method, PML

CLC Number: