Abstract
Variable substitutions are introduced to the single layer potential equations such that the order of pseudo-differential operator is changed from minus one to plus one. Though the condition number remains the same order after such a variable substitution, the frequencies of higher and lower eigenfunctions are switched. The multigrid iteration is shown to be an optimal order solver for the resulting linear systems of boundary element equations. Two types of variable substitutions are suggested. Numerical tests are presented showing efficiency of both methods, and supporting the theory.
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