Quadratic spline collocation method and efficient preconditioner for the Helmholtz equation with Robbins boundary conditions
نویسندگان
چکیده
Numerical solutions of the Helmholtz equation with Robbins boundary conditions are researched using the quadratic spline collocation method. By reordering the unknowns, we obtain a 2×2 block linear system where the two diagonal sub-matrices are block tridiagonal. For the obtained linear system, we introduce a two-step preconditioner using the block polynomial preconditioner. Theoretical analysis shows this preconditioner can largely gather the eigenvalues. Numerical examples are presented to demonstrate our method from two aspects: testing the errors and checking the efficiency of the two-level preconditioner.
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