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  • 1
    Electronic Resource
    Electronic Resource
    A finite-element capacitance matrix method for exterior Helmholtz problems (1996)
    Springer
    Numerische Mathematik 75 (1996), S. 175-204 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):65N10, 65F30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. We introduce an algorithm for the efficient numerical solution of exterior boundary value problems for the Helmholtz equation. The problem is reformulated as an equivalent one on a bounded domain using an exact non-local boundary condition on a circular artificial boundary. An FFT-based fast Helmholtz solver is then derived for a finite-element discretization on an annular domain. The exterior problem for domains of general shape are treated using an imbedding or capacitance matrix method. The imbedding is achieved in such a way that the resulting capacitance matrix has a favorable spectral distribution leading to mesh independent convergence rates when Krylov subspace methods are used to solve the capacitance matrix equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050236
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Equivalent iterative methods for p-cyclic matrices (2000)
    Springer
    Numerical algorithms 25 (2000), S. 161-180 
    Details
    ISSN: 1572-9265
    Keywords: SOR ; cyclic reduction ; Krylov subspace methods ; GMRES ; FOM ; p-cyclic matrices ; equivalent iterative methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract An overview is given of the simplifications which arise when p-cyclic systems are solved by iterative methods. Besides the classic iterative methods, we treat the Chebyshev semi-iterative method and the OR and MR variants of the class of Krylov subspace methods. Particular emphasis is given to equivalent iterations applied to the cyclically reduced system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1016666622895
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    Paper (German National Licenses)
    Fulltext
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