Diomres (k,m): An efficient method based on Krylov subspaces to solve big, dispersed, unsymmetrical linear systems
- Universidad Michoacana SNH, Michoacan (Mexico)
In geothermal simulation processes, MULKOM uses Integrated Finite Differences to solve the corresponding partial differential equations. This method requires to resolve efficiently big linear dispersed systems of non-symmetrical nature on each temporal iteration. The order of the system is usually greater than one thousand its solution could represent around 80% of CPU total calculation time. If the elapsed time solving this class of linear systems is reduced, the duration of numerical simulation decreases notably. When the matrix is big (N{ge}500) and with holes, it is inefficient to handle all the system`s elements, because it is perfectly figured out by its elements distinct of zero, quantity greatly minor than N{sup 2}. In this area, iteration methods introduce advantages with respect to gaussian elimination methods, because these last replenish matrices not having any special distribution of their non-zero elements and because they do not make use of the available solution estimations. The iterating methods of the Conjugated Gradient family, based on the subspaces of Krylov, possess the advantage of improving the convergence speed by means of preconditioning techniques. The creation of DIOMRES(k,m) method guarantees the continuous descent of the residual norm, without incurring in division by zero. This technique converges at most in N iterations if the system`s matrix is symmetrical, it does not employ too much memory to converge and updates immediately the approximation by using incomplete orthogonalization and adequate restarting. A preconditioned version of DIOMRES was applied to problems related to unsymmetrical systems with 1000 unknowns and less than five terms per equation. We found that this technique could reduce notably the time needful to find the solution without requiring memory increment. The coupling of this method to geothermal versions of MULKOM is in process.
- Research Organization:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- DOE Contract Number:
- AC03-76SF00098
- OSTI ID:
- 107199
- Report Number(s):
- LBL-37200; CONF-9503110-; ON: DE95014788; TRN: 95:006737-0039
- Resource Relation:
- Conference: TOUGH 95: transport of unsaturated ground water and heat workshop, Berkeley, CA (United States), 20-22 Mar 1995; Other Information: PBD: Mar 1995; Related Information: Is Part Of Proceedings of the TOUGH Workshop `95 Lawrence Berkeley Laboratory, Berkeley, California, March 20--22, 1995; Pruess, K. [ed.]; PB: 380 p.
- Country of Publication:
- United States
- Language:
- English
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