Parallel-In-Time Magnus Integrators

Parallel-in-time Magnus Integrators

Magnus integrators are a subset of geometric integration methods for the numerical solution of ordinary differential equations that conserve certain invariants in the numerical solution. This paper explores temporal parallelism of Magnus integrators, particularly in the context of nonlinear problems. The approach combines the concurrent computation of matrix commutators and exponentials within ...

Implicit Parallel Time Integrators

In this work, we discuss a family of parallel implicit time integrators for multi-core and potentially multinode or multi-gpgpu systems. The method is an extension of Revisionist Integral Deferred Correction (RIDC) by Christlieb, Macdonald and Ong (SISC-2010) which constructed parallel explicit time integrators. The key idea is to re-write the defect correction framework so that, after initial ...

On Magnus Integrators for Time-Dependent Schrödinger Equations

Parallel Semi-Implicit Time Integrators

In this paper, we further develop a family of parallel time integrators known as Revisionist Integral Deferred Correction methods (RIDC) to allow for the semiimplicit solution of time dependent PDEs. Additionally, we show that our semi-implicit RIDC algorithm can harness the computational potential of multiple general purpose graphical processing units (GPUs) in a single node by utilizing exist...

Magnus integrators on multicore CPUs and GPUs

In the present paper we consider numerical methods to solve the Schr\"odinger equation with a time dependent Hamiltonian. We will consider both short-range interactions, which lead to evolution equations involving sparse matrices, and long-range interactions, which lead to dense matrices. Both of these settings show very different computational characteristics. We use Magnus integrators for tim...