Please use this identifier to cite or link to this item:
For citation please use:
Main Title: Time-stepping methods for the simulation of the self-assembly of nano-crystals in MATLAB on a GPU
Author(s): Korzec, Maciek
Ahnert, Tobias
Type: Research Paper
Abstract: Partial differential equations describing the patterning of thin crystalline films are typically of fourth or sixth order, they are quasi- or semilinear and they are mostly defined on simple geometries such as rectangular domains. For the numerical simulation of these kind of problems spectral methods are an efficient approach. We apply several implicit-explicit schemes to one recently derived PDE that we express in terms of coefficients of trigonometric interpolants. While the simplest IMEX scheme turns out to have the mildest step-size restriction, higher order SBDF schemes tend to be more unstable and exponential time integrators are fastest for the calculation of very accurate solutions. We implemented a reduced model in the EXPINT package syntax and compared various exponential schemes. A convexity splitting approach was employed to stabilize the SBDF1 scheme. We show that accuracy control is crucial when using this idea, therefore we present a time-adaptive SBDF1/SBDF1-2-step method that yields convincing results reflecting the change in timescales during topological changes of the nanostructures. The implementation of all presented methods is carried out in MATLAB. We used the open source GPUmat package to gain up to 5-fold runtime benefits by carrying out calculations on a low-cost GPU without having to prescribe any knowledge in low-level programming or CUDA implementations and found comparable speedups as with MATLAB's PCT or with GPUmat run on Octave.
Subject(s): quantum dot self-assembly
GPU computing
pseudospectral method
convexity splitting
exponential integrators
Issue Date: 12-Mar-2013
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 65M70 Spectral, collocation and related methods
65L06 Multistep, Runge-Kutta and extrapolation methods
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2013, 07
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

Files in This Item:
Format: Adobe PDF | Size: 1.57 MB
DownloadShow Preview

Item Export Bar

Items in DepositOnce are protected by copyright, with all rights reserved, unless otherwise indicated.