Combining p-multigrid and Multigrid Reduction in Time methods to obtain a scalable solver for Isogeometric Analysis

The use of sequential time integration schemes becomes more and more the bottleneck within large-scale computations due to a stagnation of processor’s clock speeds. In this study, we combine the parallel-in-time Multigrid Reduction in Time method with a p-multigrid method to obtain a scalable solver specifically designed for Isogeometric...

Multigrid Reduced in Time for Isogeometric Analysis

Isogeometric Analysis (IgA) can be seen as the natural extension of the Finite Element Method (FEM) to high-order B-spline basis functions. Combined with a time inte- gration scheme within the method of lines, IgA has become a viable alternative to FEM for time-dependent problems. However, as processors' clock speeds are no longer increasing but...

Towards accuracy and scalability: Combining Isogeometric Analysis with deflation to obtain scalable convergence for the Helmholtz equation

Finding fast yet accurate numerical solutions to the Helmholtz equation remains a challenging task. The pollution error (i.e. the discrepancy between the numerical and analytical wave number k) requires the mesh resolution to be kept fine enough to obtain accurate solutions. A recent study showed that the use of Isogeometric Analysis (IgA)...

The role of PDE-based parameterization techniques in gradient-based IGA shape optimization applications

This paper proposes a shape optimization algorithm based on the principles of Isogeometric Analysis (IGA) in which the parameterization of the geometry enters the problem formulation as an additional PDE-constraint. Inspired by the isoparametric principle of IGA, the parameterization and the governing state equation are treated using the same...

Spline-based meshing techniques for industrial applications

Isogeometric Analysis (IgA) has become an accepted framework for the mod-elling, simulation and optimization (MSO) of engineering processes. However, the fully automatized generation of analysis-suitable parameterizations of geometries as they arise in practical workflows is still a challenging task, which often requires application-specific...

Efficient Multigrid based solvers for isogeometric analysis

Introduced in [1], Isogeometric Analysis (IgA) has become widely accepted in academia and industry. However, solving the resulting linear systems remains a challenging task. For instance, the condition number of the Poisson operator scales quadratically with the mesh width h, but, in contrast to standard Finite Elements, exponentially with the...