The ability to analyze system properties for large scale systems is an important part of modern engineering. Although computer power increases constantly, there is still need to develop tailored methods that are able to handle large scale systems, since sometimes standard methods cannot handle the large scale problems that occur. In this thesis the focus is on system analysis, in particular ana...

Tantrix (Tantrix R ⃝ is a registered trademark of Colour of Strategy Ltd. in New Zealand, and of TANTRIX JAPAN in Japan, respectively, under the license of M. McManaway, the inventor.) is a puzzle to make a loop by connecting lines drawn on hexagonal tiles, and the objective of this research is to solve it by a computer. For this purpose, we first give a problem setting of solving Tantrix as ma...

Iterative solver with preconditioning is the most powerful choice for large-scale scientific computation, especially for the parallel computing. In nonlinear problems such as contact simulations for geophysics, the condition numbers of the coefficient matrices are usually large due to special constraint conditions. The result is slow convergence of the iterative solver. In this study, a new pre...

This paper describes a parallel iterative solver for nite element discretisations of elliptic partial diierential equations on 2D and 3D domains using unstructured grids. The discretisation of the PDE is assumed to be given in the form of element stiiness matrices and the solver is automatic in the sense that it requires minimal additional information about the PDE and the geometry of the domai...

This paper presents the fast preconditioned iterative solution to large sparse linear systems arising from the application of Newton and quasi-Newton methods to fully coupled elastohydrodynamic lubrication line and point contact problems. The new blockwise preconditioner that is presented combines the use of multigrid for the linear elasticity block and a separate approximation to precondition ...

We present an iterative primal-dual solver for nonconvex equality-constrained quadratic optimization subproblems. The solver constructs the primal and dual trial steps from the subspace generated by the generalized Arnoldi procedure used in flexible GMRES (FGMRES). This permits the use of a wide range of preconditioners for the primal-dual system. In contrast with FGMRES, the proposed method se...

This paper describes multi-thread parallel open source JAVA implementation of alternating directions isogeometric L2 projections solver. The solver enables for fast numerical simulations of time-dependent problems. To apply our solver, the time-dependent problem must be discretized using isogeometric finite element method with B-spline basis functions in the spatial domain. The problem is solve...

The shallow water magnetohydrodynamic system describes the thin layer evolution of the solar tachocline. It is obtained from the three dimensional incompressible magnetohydrodynamic system similarly as the classical shallow water system is obtained from the incompressible NavierStokes equations. The system is hyperbolic and has two additional waves with respect to the shallow water system, the ...

The multi-level fast multipole algorithm (MLFMA) is traditionally employed in the context of an iterative matrix solver, in which the MLFMA is utilized to implement the underlying matrix product with N log N complexity, where N represents the number of unknowns. The total computational complexity of such an approach is order PN log N, where P represents the number of iterations required for ite...