Computer Science NASC Seminar

Sweeping Preconditioners for the Helmholtz Equation

Lexing Ying, University of Texas, Austin

October 22, 2010 10:00AM
Warren Weaver Hall, Room 1302
251 Mercer Street
New York, NY, 10012-1110

Fall 2010 NASC Seminars Calendar


Numerical solution of the variable coefficient Helmholtz equation in the high frequency regime is a challenging computational problem due to the indefiniteness of the operator and the large size of the discrete system. In this talk, we introduce the sweeping preconditioners for the rapid solution of the variable coefficient Helmholtz equation. The novelties of this new class of preconditioners are a specific order of eliminating the unknowns and efficient representations of the Schur complement matrices. For a problem with N unknowns, these preconditioners take essentially O(N) steps to apply, give iteration numbers that are independent of the frequency, and hence provide a linear-complexity method for solving the variable coefficient Helmholtz equation. This is a joint work with Bjorn Engquist.

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