The Indefinite Helmholtz Equation
In this chapter, we apply BBMG and AutoMUG versions to the indefinite Helmholtz equation, discretized on a uniform rectangular grid. Using ideas from AutoMUG, the transfer operators in the BBMG version are also designed to agree with the nearly singular eigenfunction of the original PDE. We also show how to compute the spectrum of the iteration matrix in some model cases. This analysis helps in the design of the multigrid method.
KeywordsDirichlet Boundary Condition Coarse Grid Spectral Radius Helmholtz Equation Multigrid Method
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