Problems of mechanics may be described by partial differential equations. To be solved with computers, they have to be discretized, e.g. with the popular Finite Element Method (FEM). We typically get large sparse linear systems of equations, but in case of constrained problems such as contact problems of mechanics, quadratic programming problems (QPs) arise. QPs also arise in other disciplines like least-squares regression, data fitting, data mining, support vector machines, control systems and many others.
Large scale problems that are not solvable on usual personal computers can be solved only in parallel on supercomputers. Domain decomposition methods (DDM) come here into play. They solve an original problem by splitting it into smaller subdomain problems that are independent, allowing natural parallelization.
Finite Element Tearing and Interconnecting (FETI) methods form a successful subclass of DDM. They belong to non-overlapping methods and combine iterative and direct solvers. FETI methods allow highly accurate computations scaling up to tens of thousands of processors.
Due to limitations of commercial packages, problems often have to be adapted to be solvable. This is an expensive process and results reflect less accurately physical phenomena. Moreover, it takes a long time before the most recent numerical methods needed for HPC are implemented into such packages.
These issues lead us to establish the PERMON (Parallel, Efficient, Robust, Modular, Object-oriented, Numerical) toolbox. It makes use of most recent theoretical results in discretization techniques, quadratic programming algorithms, and domain decomposition methods. It incorporates our own codes, and makes use of renowned open source libraries. We focus on engineering applications (linear elasticity, contact problems, elasto-plasticity, shape optimization and others) as well as altruistic ones (medical imaging, ice-sheet melting modelling, climate changes modelling and others).