# Some iterative Poisson solvers applied to numerical solution of the model fourth-order elliptic problem

Aplikace matematiky (1985)

- Volume: 30, Issue: 3, page 176-186
- ISSN: 0862-7940

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topVajteršic, Marián. "Some iterative Poisson solvers applied to numerical solution of the model fourth-order elliptic problem." Aplikace matematiky 30.3 (1985): 176-186. <http://eudml.org/doc/15396>.

@article{Vajteršic1985,

abstract = {The numerical solution of the model fourth-order elliptic boundary value problem in two dimensions is presented. The iterative procedure in which the biharmonic operator is splitted into two Laplace operators is used. After formulating the finite-difference approximation of the procedure, a formula for the evaluation of the transformed iteration vectors is developed. The Jacobi semi-iterative, Richardson and A.D.I. iterative Poisson solvers are applied to compute one transformed iteration vector. By the efficient use of the decomposition property of the corresponding iteration matrices, the fast Fourier transform algorithm needs to be applied twice in the evaluation of one iteration vector. The asymptotic number of operations for the sequential computation is $5n^2 log_2 n$, where $n^2$ is the number of interior grid points in the unit square. The result of$7 \ log_2 \ n$ parallel steps for the parallel computation on an SIMD machine with $n^2$ processors is so far the best one.},

author = {Vajteršic, Marián},

journal = {Aplikace matematiky},

keywords = {fourth-order; biharmonic operator; Laplace operators; Jacobi semi- iterative; Richardson; A.D.I.; fast Fourier transform; SIMD machine; fourth-order; biharmonic operator; Laplace operators; Jacobi semi- iterative; Richardson; A.D.I.; fast Fourier transform; SIMD machine},

language = {eng},

number = {3},

pages = {176-186},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Some iterative Poisson solvers applied to numerical solution of the model fourth-order elliptic problem},

url = {http://eudml.org/doc/15396},

volume = {30},

year = {1985},

}

TY - JOUR

AU - Vajteršic, Marián

TI - Some iterative Poisson solvers applied to numerical solution of the model fourth-order elliptic problem

JO - Aplikace matematiky

PY - 1985

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 30

IS - 3

SP - 176

EP - 186

AB - The numerical solution of the model fourth-order elliptic boundary value problem in two dimensions is presented. The iterative procedure in which the biharmonic operator is splitted into two Laplace operators is used. After formulating the finite-difference approximation of the procedure, a formula for the evaluation of the transformed iteration vectors is developed. The Jacobi semi-iterative, Richardson and A.D.I. iterative Poisson solvers are applied to compute one transformed iteration vector. By the efficient use of the decomposition property of the corresponding iteration matrices, the fast Fourier transform algorithm needs to be applied twice in the evaluation of one iteration vector. The asymptotic number of operations for the sequential computation is $5n^2 log_2 n$, where $n^2$ is the number of interior grid points in the unit square. The result of$7 \ log_2 \ n$ parallel steps for the parallel computation on an SIMD machine with $n^2$ processors is so far the best one.

LA - eng

KW - fourth-order; biharmonic operator; Laplace operators; Jacobi semi- iterative; Richardson; A.D.I.; fast Fourier transform; SIMD machine; fourth-order; biharmonic operator; Laplace operators; Jacobi semi- iterative; Richardson; A.D.I.; fast Fourier transform; SIMD machine

UR - http://eudml.org/doc/15396

ER -

## References

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