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HSL_MP62 Symmetric finite-element system: multiple-front method

The module HSL_MP62 uses the multiple front method to solve sets of symmetric positive-definite finite-element equations AX = B that have been divided into non-overlapping subdomains. The HSL routines MA62 and MA72 are used with MPI for message passing.

TThe 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. 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 (1) 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.