Massively Parallel Quadratic Programming Solvers with Applications in Mechanics
Massively Parallel Quadratic Programming Solvers with Applications in Mechanics Ing. V´aclav Hapla Doctoral Thesis Department of Applied Mathematics Faculty of Electrical Engineering and Computer Science VSBˇ – Technical University of Ostrava Ostrava 2016 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 Dost´al, 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 con- nected to practical implementation. Original topics include QP transforms, implicit orthonor- malization of equality constraints, and a minor modification of SMALBE shortening its termi- nation phase considerably. Second part, Implementation, deals with the massively parallel implementation of the afore- mentioned 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 decomposi- tion. These libraries make use of and extend PETSc, an open source software framework for numerical computing. Performance of PERMON is demonstrated on several numerical experi- ments. Keywords quadratic programming, QP, domain decomposition methods, FETI, augmented Lagrangian, SMALBE, MPRGP, contact problems, structure mechanics, PERMON, PermonQP, Permon- FLLOP, PETSc Abstrakt Tato dizertaˇcn´ıpr´ace se zamˇeˇruje na praktick´eˇreˇsen´ırozs´ahl´ych kontaktn´ıch ´uloh struktur´aln´ı mechaniky pˇres odvozenou ´ulohu kvadratick´eho programov´an´ı(QP).
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