USING A REDUCED NUMBER OF LAGRANGE MULTIPLIERS FOR ASSEMBLING PARALLEL INCOMPLETE FIELD FINITE-ELEMENT APPROXIMATIONS

被引:34
作者
FARHAT, C
GERADIN, M
机构
[1] UNIV COLORADO,CTR SPACE STRUCT & CONTROLS,BOULDER,CO 80309
[2] STATE UNIV LIEGE,TECH AERONAUT & SPATIALES LAB,B-4000 LIEGE,BELGIUM
[3] OFF NATL ETUD & RECH AEROSP,CONSEILLER SCI,F-92322 CHATILLON,FRANCE
关键词
Differential equations - Mechanics - Structural analysis - Variational techniques;
D O I
10.1016/0045-7825(92)90050-T
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
A domain decomposition algorithm based on a hybrid variational principle was proposed by Farhat and Roux for the parallel finite element solution of self-adjoint elliptic partial differential equations. First, the spatial domain was partitioned into a set of totally disconnected subdomains and an incomplete finite element solution was computed in each of these subdomains. Next, a number of Lagrange multipliers equal to the number of degrees of freedom located at the binding interface were introduced to enforce compatibility constraints between the independent local finite element approximations. For structural and mechanical problems, the resulting algorithm was shown to outperform the conventional method of substructures, especially on parallel processors. Here, the use of a much lower number of Lagrange multipliers for interconnecting the incomplete field finite element solutions is investigated. When accuracy is preserved, this approach drastically reduces the computational complexity of the Schur-complement-like coupling system that is associated with the interface region and significantly enhances the overall performance of the methodology. Finite element procedures for both global and piecewise polynomial approximations of the Lagrange multipliers are derived. Finally, some numerical results obtained for structural example problems that validate the main idea and highlight its advantages are presented.
引用
收藏
页码:333 / 354
页数:22
相关论文
共 10 条
[1]  
CONTE SD, 1980, ELEMENTARY NUMERICAL, P288
[2]  
DORR MR, 1988, UCRL98532 LAWR LIV N
[3]   A NEW FINITE-ELEMENT CONCURRENT COMPUTER-PROGRAM ARCHITECTURE [J].
FARHAT, C ;
WILSON, E .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1987, 24 (09) :1771-1792
[4]   A METHOD OF FINITE-ELEMENT TEARING AND INTERCONNECTING AND ITS PARALLEL SOLUTION ALGORITHM [J].
FARHAT, C ;
ROUX, FX .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1991, 32 (06) :1205-1227
[5]  
FARHAT C, 1989, COMPUTATIONAL STR AD, V16, P35
[7]  
Nour-Omid B, 1987, PARALLEL COMPUT, P209
[8]  
Pian T.H., 1972, MATH FDN FINITE ELEM, P671
[9]  
STORAASLI OO, 1989, 30 STRUCT STRUCT DYN, P859
[10]  
ZIENKIEWICZ OC, 1989, FINITE ELEMENT METHO, V1, P373