Parallel finite element splitting-up method for parabolic problems
Tai, X.-C., Neittaanmäki, P. (1991). Parallel finite element splitting-up method for parabolic problems. Numerical Methods for Partial Differential Equations, 7 (3), 209-225. doi:10.1002/num.1690070302
Published inNumerical Methods for Partial Differential Equations
An efficient method for solving parabolic systems is presented. The proposed method is based on the splitting‐up principle in which the problem is reduced to a series of independent 1D problems. This enables it to be used with parallel processors. We can solve multidimensional problems by applying only the 1D method and consequently avoid the difficulties in constructing a finite element space for multidimensional problems. The method is suitable for general domains as well as rectangular domains. Every 1D subproblem is solved by applying cubic B‐splines. Several numerical examples are presented.
ISSN Search the Publication Forum0749-159X
MetadataShow full item record
Showing items with similar title or keywords.
A parallel FE-splitting up method to parabolic problems Tai, Xue-Cheng; Neittaanmäki, Pekka (University of Jyväskylä, 1989)
On the finite element method for time-harmonic acoustic boundary value problems Neittaanmäki, Pekka; Picard, Rainer (Pergamon Press, 1981)The time harmonic acoustic boundary value problem in a smooth, bounded domain G of R2 is considered as a first order system. The optimal asymptotic L2(G) and H1(G)-error estimates 0(h2) and 0(h) resp. are derived for a ...
A nontraditional approach for solving the Neumann problem by the finite element method Křižek, Michal; Neittaanmäki, Pekka; Vondrák, Miroslav (Sociedade Brasileira de Matemática Aplicada e Computacional, 1992)We present a new variational formulation of a second order order elliptic problem with the Neumann boundary conditions. This formulation does not require any quotient spaces and is advisable for finite element approximations.
A parallel splitting-up method for partial differential equations and its applications to Navier-Stokes equations Lu, T.; Neittaanmäki, P.; Tai, X.-C. (AFCET Gauhtier-Villars, 1992)The tradìtíonal splitting-up method or fractíonal step method is stuítable for sequentìal compulìng. Thís means that the computing of the present fractional step needs the value of the previous fractional steps. In thìs ...
A parallel splitting up method and its application to Navier-Stokes equations Lu, T.; Neittaanmäki, Pekka; Tai, Xue-Cheng (Pergamon Press, 1991)A parallel splitting-up method (or the so called alternating-direction method) is proposed in this paper. The method not only reduces the original linear and nonlinear problems into a series of one dimensional linear ...