Log In Sign Up

Combining p-multigrid and multigrid reduced in time methods to obtain a scalable solver for Isogeometric Analysis

by   Roel Tielen, et al.

Isogeometric Analysis (IgA) has become a viable alternative to the Finite Element Method (FEM) and is typically combined with a time integration scheme within the method of lines for time-dependent problems. However, due to a stagnation of processors clock speeds, traditional (i.e. sequential) time integration schemes become more and more the bottleneck within these large-scale computations, which lead to the development of parallel-in-time methods like the Multigrid Reduced in Time (MGRIT) method. Recently, MGRIT has been succesfully applied by the authors in the context of IgA showing convergence independent of the mesh width, approximation order of the B-spline basis functions and time step size for a variety of benchmark problems. However, a strong dependency of the CPU times on the approximation order was visible when a standard Conjugate Gradient method was adopted for the spatial solves within MGRIT. In this paper we combine MGRIT with a state-of the-art solver (i.e. a p-multigrid method), specifically designed for IgA, thereby significantly reducing the overall computational costs of MGRIT. Furthermore, we investigate the performance of MGRIT and its scalability on modern copmuter architectures.


Parallel block preconditioners for virtual element discretizations of the time-dependent Maxwell equations

The focus of this study is the construction and numerical validation of ...

Magnetic Field Simulations Using Explicit Time Integration With Higher Order Schemes

A transient magneto-quasistatic vector potential formulation involving n...

Numerical Analysis of History-dependent Variational-hemivariational Inequalities

In this paper, numerical analysis is carried out for a class of history-...

Efficient multiscale methods for the semiclassical Schrödinger equation with time-dependent potentials

The semiclassical Schrödinger equation with time-dependent potentials is...

Isoparametric unfitted BDF – Finite element method for PDEs on evolving domains

We propose a new discretization method for PDEs on moving domains in the...

Hierarchical Optimization Time Integration for CFL-rate MPM Stepping

We propose Hierarchical Optimization Time Integration (HOT) for efficien...