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HSL_MP42 Unsymmetric finite-element system: multiple-front method, element entry

The module HSL_MP42 uses the multiple front method to solve sets of finite-element equations AX = B that have been divided into non-overlapping subdomains. The HSL routines MA42 and MA52 are used with MPI for message passing.

The coefficient matrix A must be of the form

A = k=1mA(k)

where the summation is over finite elements. The element matrix A(k) is nonzero only in those rows and columns which correspond to variables in the k-th element. The right-hand side(s) B may optionally be in the form

B = k=1mB(k)

where B(k) is nonzero only in those rows which correspond to variables in element k.

In the multiple front method, a frontal decomposition is performed on each subdomain separately. Thus, on each subdomain, L and U factors are computed. Once all possible eliminations have performed within a subdomain, there remain the interface variables, which are shared by more than one subdomain together with any variables that are not eliminated because of stability or efficiency considerations. If Fi is the remaining frontal matrix for subdomain i, and Ci is the corresponding right-hand side matrix, then the remaining problem is

FY = C, (1)

where F = iFi and C = iCi. By treating each Fi as an element matrix, the interface problem (3) is also solved by the frontal method. Once (1) has been solved, back-substitution on the subdomains completes the solution.

The element data and/or the matrix factors are optionally held in direct-access files.