ASIL - Advanced Solvers Integrated Library

The project ASIL (Advanced Solvers Integrated Library) is concerned with the development of efficient and robust solution methods for large linear systems and of an associated software library.

Solving large linear systems is one of the main tasks in the simulation of phenomena from natural sciences, engineering, life science, finance, economics, and technology, as this step determines the complexity of the whole simulation process. Thus, the availability of highly scalable as well as efficient and robust solvers is of crucial relevance for usability of high performance parallel computers.

The development is realized in the kernel of the solution process of large systems. Filtering algebraic multigrid methods are improved and combined with H-matrix techniques for that reason. At the same time, we will develop and realize methods for further problems like multiscale, eigenvalue or optimization problems. Thus, a new software library for the solution of very large problems will be available at the end of the project ASIL.

The ASIL project is a cooperation between our group,  Prof. Dr. G. Wittum at  Goethe Center for Scientific Computing, Prof.Dr. W. Hackbusch at the Max-Planck-Institute for Mathematics in the Sciences  in Leipzig, Prof. Dr. V. Schulz at  the University of Trier, and Prof. Dr. C. Wieners the Institut für Wissenschaftliches Rechnen und Mathematische Modellierung (IWRMM) at the Karlsruhe Institute of Technology, and Prof.Dr. M. Resch at  the High performance Computing Center Stuttgart

Nonsmooth and nonlinear structures emerge in numerous applications in a natural way. Inequality constraints, nonlinear material behavior or crack and fracture development are examples for these nonlinearities. Their numerical treatment requires the development of generic multiscale methods, which allow for the uniform treatment of nonlinearly coupled effects on different time and length scales. In the last decades, nonsmooth and nonlinear multilevel methods turned out to be very robust and efficient for such problems. Thus, as an extension of recent results in the area of multiscale methods in our group, generic multiscale methods, which allow for the massively parallel simulation of strongly nonlinear and nonsmooth multiscale problems, are developed and implemented in this project. Typical applications are, e.g. crack nucleation and frictional contact with non-standard friction laws.