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  • 1
    Electronic Resource
    Electronic Resource
    On a fast direct elliptic solver by a modified Fourier method (1997)
    Springer
    Numerical algorithms 15 (1997), S. 287-313 
    Details
    ISSN: 1572-9265
    Keywords: Helmholtz equation ; Fourier method ; fast solver ; subtraction technique ; corner singularities
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We describe high order numerical algorithms for the solution of second order elliptic equations in rectangular domains. These algorithms are based on the Fourier method in combination with a subtraction procedure. The singularities at the corner points, arising due to non-smoothness of the boundaries, are treated explicitly using properly constructed singular corner functions. The present algorithm is a generalization of the Fast Poisson Solver developed in our previous paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019106223154
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  • 2
    Electronic Resource
    Electronic Resource
    Spectral multidomain technique with Local Fourier Basis II: Decomposition into cells (1994)
    Springer
    Journal of scientific computing 9 (1994), S. 311-326 
    Details
    ISSN: 1573-7691
    Keywords: Spectral method ; multidomain method ; Fourier method ; parallel processing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract The spectral multidomain method for the solution of 2-D elliptic and parabolic PDE's is developed. The computational region is decomposed into rectangular cells. A Local Fourier Basis technique is implemented for the discretization in space. Such a technique enables the global (typically ∼104–105) matching relations for the interface unknows to be decoupled into a set of relations for only few interface points at a time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01575035
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  • 3
    Electronic Resource
    Electronic Resource
    Spectral multidomain technique with Local Fourier Basis (1993)
    Springer
    Journal of scientific computing 8 (1993), S. 135-149 
    Details
    ISSN: 1573-7691
    Keywords: Spectral methods ; multidomain ; parallel processing ; Fourier method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract A novel domain decomposition method for spectrally accurate solutions of PDEs is presented. A Local Fourier Basis technique is adapted for the construction of the elemental solutions in subdomains.C 1 continuity is achieved on the interfaces by a matching procedure using the analytical homogeneous solutions of a one dimensional equation. The method can be applied to the solution of elliptic problems of the Poisson or Helmholtz type as well as to time discretized parabolic problems in one or more dimensions. The accuracy is tested for several stiff problems with steep solutions. The present domain decomposition approach is particularly suitable for parallel implementations, in particular, on MIMD type parallel machines.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01060869
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