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Burrage, Kevin

doi:10.1023/a:1018997130884

Cited by 27 publications

(7 citation statements)

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“…would indicate sequentially solving the full initial value problem in serial using the time stepper denoted by F δt . In order to parallelise the numerical integration of (1), Parareal and other so-called parallel-across-the-steps methods [22] introduce a decomposition of the time interval [0, T ] into time-slices [t p , t p+1 ], p = 0, . .…”

Section: The Method: Pararealmentioning

confidence: 99%

Shared Memory Pipelined Parareal

Ruprecht

2017

Lecture Notes in Computer Science

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Abstract. For the parallel-in-time integration method Parareal, pipelining can be used to hide some of the cost of the serial correction step and improve its efficiency. The paper introduces an OpenMP implementation of pipelined Parareal and compares it to a standard MPI-based variant. Both versions yield almost identical runtimes, but, depending on the compiler, the OpenMP variant consumes about 7% less energy and has a significantly smaller memory footprint. However, its higher implementation complexity might make it difficult to use in legacy codes and in combination with spatial parallelisation.

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Section: The Method: Pararealmentioning

confidence: 99%

Shared Memory Pipelined Parareal

Ruprecht

2017

Lecture Notes in Computer Science

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“…Note that in order to compute larger time-steps, we can choose larger values for R 1 in the conformal map (12). Choosing larger values of R 1 , however, is likely to increase the approximation error .…”

Section: Step-size Requirementsmentioning

confidence: 99%

“…One promising remedy is the application of parallel-in-time integration techniques. They expose parallelism also in the temporal domain, either within each time-step, referred to as parallelization across the method, or by computing multiple time-steps simultaneously, referred to as parallelization across the steps [12].…”

Section: Introductionmentioning

confidence: 99%

Time-parallel simulation of the Schrödinger Equation

Rittich,

Speck

2019

Preprint

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The numerical simulation of the time-dependent Schrödinger equation for quantum systems is a very active research topic. Yet, resolving the solution sufficiently in space and time is challenging and mandates the use of modern high-performance computing systems. While classical parallelization techniques in space can reduce the runtime per time-step, novel parallel-in-time integrators expose parallelism in the temporal domain. They work, however, not very well for wave-type problems such as the Schrödinger equation. One notable exception is the rational approximation of exponential integrators. In this paper we derive an efficient variant of this approach suitable for the complex-valued Schrödinger equation. Using the Faber-Carathéodory-Fejér approximation, this variant is already a fast serial and in particular an efficient time-parallel integrator. It can be used to augment classical parallelization in space and we show the efficiency and effectiveness of our method along the lines of two challenging, realistic examples.

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“…The technique of parallelism across the system is via the decomposition of a problem into sub-problems which can then be solved in parallel with the processors communicating as appropriate. Parallelism across the step in which generation integration steps are perform concurrently with a given numerical method (Burrage (1997), Amodio and Brugnano (2008) for more details)…”

Section: Introductionmentioning

confidence: 99%

A Diagonally Implicit Runge-Kutta-Nystrom (Rkn) Method for Solving Second Order Odes on Parallel Computers

Imoni

2020

FJS

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In this paper, diagonally implicit Runge-Kutta-Nystrom (RKN) method of high-order for the numerical solution of second order ordinary differential equations (ODE) possessing oscillatory solutions to be used on parallel computers is constructed. The method has the properties of minimized local truncation error coefficients as well as possessing non-empty interval of periodicity, thus suitable for oscillatory problems. The method was tested with standard test problems from the literature and numerical results compared with the analytical solution to show the advantage of the algorithm

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Cited by 27 publications

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Shared Memory Pipelined Parareal

Shared Memory Pipelined Parareal

Time-parallel simulation of the Schrödinger Equation

A Diagonally Implicit Runge-Kutta-Nystrom (Rkn) Method for Solving Second Order Odes on Parallel Computers

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