A damping preconditioner for time-harmonic wave equations in fluid and elastic material
Journal of Computational Physics
Equation-based interpolation and incremental unknowns for solving the Helmholtz equation
Applied Numerical Mathematics
GPU implementation of a Helmholtz Krylov solver preconditioned by a shifted Laplace multigrid method
Journal of Computational and Applied Mathematics
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In many numerical procedures one wishes to improve the basic approach either to improve efficiency or else to improve accuracy. Frequently this is based on an analysis of the properties of the discrete system being solved. Using a linear algebra approach one then improves the algorithm. We review methods that instead use a continuous analysis and properties of the differential equation rather than the algebraic system. We shall see that frequently one wishes to develop methods that destroy the physical significance of intermediate results. We present cases where this procedure works and others where it fails. Finally we present the opposite case where the physical intuition can be used to develop improved algorithms.