Massively Parallel Quadratic Programming Solvers with Applications in Mechanics

Abstract

This thesis focuses on practical solution of large-scale contact problems of structure mechanics by means of a derived quadratic programming (QP) formulation. An approach proposed by professor Dostál, combining a FETI-type non-overlapping domain decomposition method, the SMALBE algorithm based on augmented Lagrangians, and the MPRGP algorithm belonging to active set methods, has been adopted. This approach enjoys theoretically supported numerical scalability and a favourable potential for parallel scalability. The thesis consists of two parts: Background and Implementation.

Background is devoted to rather theoretical aspects of QP and FETI, although tightly connected to practical implementation. Original topics include QP transforms, implicit orthonormalization of equality constraints, and a minor modification of SMALBE shortening its termination phase considerably.

Second part, Implementation, deals with the massively parallel implementation of the aforementioned approach within PERMON, a new set of software libraries established by the author. The most important part, PERMON Solver Core, is formed mainly by the general-purpose QP solver PermonQP, and its extension PermonFLLOP providing support for domain decomposition. These libraries make use of and extend PETSc, an open source software framework for numerical computing. Performance of PERMON is demonstrated on several numerical experiments.