Iterative domain decomposition algorithms for the solution of singularly perturbed parabolic problems

Computers and Mathematics with Applications

Volumn 31, Issue 10, 1996, Pages 83-100

  Boglaev, I P ^a,c   Sirotkin, V V ^b  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

^b INSTITUTE OF MICROELECTRONICS TECHNOLOGY AND HIGH PURITY MATERIALS   (Russian Federation)

^c MASSEY UNIVERSITY   (New Zealand)

Author keywords

Domain decomposition method; Parallel computing; Singularly perturbed parabolic problem; Time discretization

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; ITERATIVE METHODS; PARALLEL PROCESSING SYSTEMS; PERTURBATION TECHNIQUES; PROBLEM SOLVING;

ITERATIVE DOMAIN DECOMPOSITION ALGORITHMS; SINGULARLY PERTURBED PARABOLIC PROBLEM; TIME DISCRETIZATION;

PARALLEL ALGORITHMS;

EID: 0030146210     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/0898-1221(96)00054-5     Document Type: Article

References (15)

1. N.S. Bakhvalov, Towards optimization of methods for solving boundary value problems in the presence of a boundary layer, (in Russian), Zh. Vychisl. Mat. i Mat. Fiz. 9, 841-859 (1969).
2. H.A. Schwarz, Über einige Abbildungsaufgaben, J. Reine Angew. Math. 70, 105-120 (1869).
3. th IMACS Congress on Computation and Applied Mathematics, Dublin (Edited by J.J.H. Miller and R. Vichnevetsky), pp. 522-523, (1991).
4. P.L. Lions, On the Schwarz alternating method, I, In Proc. First International Symposium on Domain Decomposition Methods for Partial Differential Equations (Edited by R. Glowinski, G.H. Golub, G.A. Meurant and J. Periaux), pp. 1-40, Society for Industrial and Applied Mathematics, Philadelphia, (1988).
5. P.L. Lions, On the Schwarz alternating method, II, In Proc. Third International Symposium on Domain Decomposition Methods for Partial Differential Equations (Edited by T.F. Chan, R. Glowinski, J. Periaux and O.B. Widlund), pp. 47-70, Society for Industrial and Applied Mathematics, Philadelphia, (1990).
6. I.P. Boglaev and V.V. Sirotkin, The solution of singularly perturbed problems via domain decomposition, Computers Math. Applic. 25 (9), 31-42 (1993).
7. I.P. Boglaev and V.V. Sirotkin, Computational method for a singular perturbation problem via domain decomposition and its parallel implementation, Applied Math. and Comput. 56, 71-95 (1993).
8. P.A. Farrell, I.P. Boglaev and V.V. Sirotkin, Parallel domain decomposition methods for semi-linear singularly perturbed differential equations, Computational Fluid Dynamics Journal 2 (4), 423-434 (1994).
9. J.D. Lavers, I.P. Boglaev and V.V. Sirotkin, The solution of 2-D eddy current problem via the domain decomposition methods on serial and parallel computers, Mathl. Comput. Modelling 21 (5), 31-48 (1995).
10. I.P. Boglaev, V.V. Sirotkin and J.D. Lavers, The computation of transient 2-D eddy current problem by domain decomposition algorithms, Mathl. Comput. Modelling 21 (3), 39-51 (1995).
11. O.A. Ladyženskaja, V.A. Solonnikov and N.N. Ural'tceva, Linear and Quasi-Linear Equations of Parabolic Type, American Math. Soc., Providence, RI, (1968).
12. G.I. Shishkin, Grid approximation of singularly perturbed boundary value problem for quasi-linear parabolic equations in the case of complete degeneracy in spatial variables, Soviet. J. Numer. Analys. Math. Modelling 6 (3), 243-261 (1991).
13. E.A. Volkov, Efficient estimates of the truncation error in the solution by finite difference of boundary problems for Laplace's and Poisson's equations on a rectangle and some triangles, (in Russian), Proc. Steklov Institute of Mathematics USSR Ac. Sci. 74, 55-85 (1966).
14. O.A. Ladyzhenskaya and N.N. Ural'tseva, Linear and Quasilinear Elliptic Equations, Academic Press, New York, (1968).
15. I.P. Boglaev, Approximate solution of a non-linear boundary value problem with a small parameter for the highest-order derivative, USSR Comput. Math, and Math. Physics 25, 30-39 (1984).