Pub Date : 2016-11-25DOI: 10.4208/cicp.OA-2016-0220
Hong Zhang, P. Zegeling
An adaptive moving mesh finite difference method is presented to solve two types of equations with dynamic capillary pressure term in porous media. One is the non-equilibrium Richards Equation and the other is the modified Buckley-Leverett equation. The governing equations are discretized with an adaptive moving mesh finite difference method in the space direction and an implicit-explicit method in the time direction. In order to obtain high quality meshes, an adaptive time-dependent monitor function with directional control is applied to redistribute the mesh grid in every time step, and a diffusive mechanism is used to smooth the monitor function. The behaviors of the central difference flux, the standard local Lax-Friedrich flux and the local Lax-Friedrich flux with reconstruction are investigated by solving a 1D modified Buckley-Leverett equation. With the moving mesh technique, good mesh quality and high numerical accuracy are obtained. A collection of one-dimensional and two-dimensional numerical experiments is presented to demonstrate the accuracy and effectiveness of the proposed method.
{"title":"A moving mesh finite difference method for non-monotone solutions of non-equilibrium equations in porous media","authors":"Hong Zhang, P. Zegeling","doi":"10.4208/cicp.OA-2016-0220","DOIUrl":"https://doi.org/10.4208/cicp.OA-2016-0220","url":null,"abstract":"An adaptive moving mesh finite difference method is presented to solve two types of equations with dynamic capillary pressure term in porous media. One is the non-equilibrium Richards Equation and the other is the modified Buckley-Leverett equation. The governing equations are discretized with an adaptive moving mesh finite difference method in the space direction and an implicit-explicit method in the time direction. In order to obtain high quality meshes, an adaptive time-dependent monitor function with directional control is applied to redistribute the mesh grid in every time step, and a diffusive mechanism is used to smooth the monitor function. The behaviors of the central difference flux, the standard local Lax-Friedrich flux and the local Lax-Friedrich flux with reconstruction are investigated by solving a 1D modified Buckley-Leverett equation. With the moving mesh technique, good mesh quality and high numerical accuracy are obtained. A collection of one-dimensional and two-dimensional numerical experiments is presented to demonstrate the accuracy and effectiveness of the proposed method.","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87505033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-11-01DOI: 10.22541/au.156754490.06103020
P. Hockett
ePSproc provides codes for post-processing results from ePolyScat (ePS), a suite of codes for the calculation of quantum scattering problems, developed and released by Luchesse & co-workers (Gianturco et al. 1994)(Natalense and Lucchese 1999)(R. R. Lucchese and Gianturco 2016). ePS is a powerful computational engine for solving scattering problems, but its inherent complexity, combined with additional post-processing requirements, ranging from simple visualizations to more complex processing involving further calculations based on ePS outputs, present a significant barrier to use for most researchers. ePSproc aims to lower this barrier by providing a range of functions for reading, processing and plotting outputs from ePS. Since ePS calculations are currently finding multiple applications in AMO physics (see below), ePSproc is expected to have significant reuse potential in the community, both as a basic tool-set for researchers beginning to use ePS, and as a more advanced post-processing suite for those already using ePS. ePSproc is currently written for Matlab/Octave, and distributed via Github: this https URL.
ePSproc提供了ePolyScat (ePS)的后处理结果的代码，ePolyScat (ePS)是Luchesse和同事(Gianturco et al. 1994)(Natalense和Lucchese 1999)开发并发布的一套用于计算量子散射问题的代码。R. Lucchese and Gianturco 2016)。ePS是解决散射问题的强大计算引擎，但其固有的复杂性，加上额外的后处理要求，从简单的可视化到更复杂的处理，包括基于ePS输出的进一步计算，对大多数研究人员来说是一个重大的障碍。epspproc旨在通过提供一系列读取、处理和绘制ePS输出的功能来降低这一障碍。由于ePS计算目前在AMO物理中有多种应用(见下文)，ePSproc有望在社区中具有重要的重用潜力，既可以作为开始使用ePS的研究人员的基本工具集，也可以作为已经使用ePS的研究人员的更高级的后处理套件。ePSproc目前是为Matlab/Octave编写的，并通过Github分发:此https URL。
{"title":"ePSproc: Post-processing suite for ePolyScat electron-molecule scattering calculations","authors":"P. Hockett","doi":"10.22541/au.156754490.06103020","DOIUrl":"https://doi.org/10.22541/au.156754490.06103020","url":null,"abstract":"ePSproc provides codes for post-processing results from ePolyScat (ePS), a suite of codes for the calculation of quantum scattering problems, developed and released by Luchesse & co-workers (Gianturco et al. 1994)(Natalense and Lucchese 1999)(R. R. Lucchese and Gianturco 2016). ePS is a powerful computational engine for solving scattering problems, but its inherent complexity, combined with additional post-processing requirements, ranging from simple visualizations to more complex processing involving further calculations based on ePS outputs, present a significant barrier to use for most researchers. ePSproc aims to lower this barrier by providing a range of functions for reading, processing and plotting outputs from ePS. Since ePS calculations are currently finding multiple applications in AMO physics (see below), ePSproc is expected to have significant reuse potential in the community, both as a basic tool-set for researchers beginning to use ePS, and as a more advanced post-processing suite for those already using ePS. ePSproc is currently written for Matlab/Octave, and distributed via Github: this https URL.","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90266893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-10-31DOI: 10.1051/epjconf/201714015007
Manuel Cárdenas-Barrantes, J. D. Muñoz, N. Araújo
Capillary rise plays a crucial role in the construction of road embankments in flood zones, where hydrophobic compounds are added to the soil to suppress the rising of water and avoid possible damage of the pavement. Water rises through liquid bridges, menisci and trimers, whose width and connectivity depends on the maximal half-length {lambda} of the capillary bridges among grains. Low {lambda} generate a disconnect structure, with small clusters everywhere. On the contrary, for high {lambda}, create a percolating cluster of trimers and enclosed volumes that form a natural path for capillary rise. Hereby, we study the percolation transition of this geometric structure as a function of {lambda} on a granular media of monodisperse spheres in a random close packing. We determine both the percolating threshold {lambda}_{c} = (0.049 pm 0.004)R (with R the radius of the granular spheres), and the critical exponent of the correlation length {nu} = (0.830 pm 0.051), suggesting that the percolation transition falls into the universality class of ordinary percolation.
{"title":"Percolation study for the capillary ascent of a liquid through a granular soil","authors":"Manuel Cárdenas-Barrantes, J. D. Muñoz, N. Araújo","doi":"10.1051/epjconf/201714015007","DOIUrl":"https://doi.org/10.1051/epjconf/201714015007","url":null,"abstract":"Capillary rise plays a crucial role in the construction of road embankments in flood zones, where hydrophobic compounds are added to the soil to suppress the rising of water and avoid possible damage of the pavement. Water rises through liquid bridges, menisci and trimers, whose width and connectivity depends on the maximal half-length {lambda} of the capillary bridges among grains. Low {lambda} generate a disconnect structure, with small clusters everywhere. On the contrary, for high {lambda}, create a percolating cluster of trimers and enclosed volumes that form a natural path for capillary rise. Hereby, we study the percolation transition of this geometric structure as a function of {lambda} on a granular media of monodisperse spheres in a random close packing. We determine both the percolating threshold {lambda}_{c} = (0.049 pm 0.004)R (with R the radius of the granular spheres), and the critical exponent of the correlation length {nu} = (0.830 pm 0.051), suggesting that the percolation transition falls into the universality class of ordinary percolation.","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75385180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-10-24DOI: 10.1103/PhysRevMaterials.1.063402
W. Xie, T. Lu, Gwo-Ching Wang, I. Bhat, Shengbai Zhang
Enhanced van der Waals (vdW) epitaxy of semiconductors on layered vdW substrate is identified as the formation of dative bonds. For example, despite that NbSe2 is a vdW layered material, first-principles calculations reveal that the bond strength at CdTe-NbSe2 interface is five times as large as that of vdW interaction at CdTe-graphene interface. The unconventional chemistry here is enabled by an effective net electron transfer from Cd dangling-bond states at CdTe surface to metallic non-bonding NbSe2 states, which is a necessary condition to activate the Cd for enhanced binding with Se.
{"title":"Enhanced van der Waals epitaxy via electron transfer-enabled interfacial dative bond formation","authors":"W. Xie, T. Lu, Gwo-Ching Wang, I. Bhat, Shengbai Zhang","doi":"10.1103/PhysRevMaterials.1.063402","DOIUrl":"https://doi.org/10.1103/PhysRevMaterials.1.063402","url":null,"abstract":"Enhanced van der Waals (vdW) epitaxy of semiconductors on layered vdW substrate is identified as the formation of dative bonds. For example, despite that NbSe2 is a vdW layered material, first-principles calculations reveal that the bond strength at CdTe-NbSe2 interface is five times as large as that of vdW interaction at CdTe-graphene interface. The unconventional chemistry here is enabled by an effective net electron transfer from Cd dangling-bond states at CdTe surface to metallic non-bonding NbSe2 states, which is a necessary condition to activate the Cd for enhanced binding with Se.","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79962705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-10-10DOI: 10.21468/SciPostPhys.2.1.003
P. Weinberg, Marin Bukov
We present a new open-source Python package for exact diagonalization and quantum dynamics of spin(-photon) chains, called QuSpin, supporting the use of various symmetries in 1-dimension and (imaginary) time evolution for chains up to 32 sites in length. The package is well-suited to study, among others, quantum quenches at finite and infinite times, the Eigenstate Thermalisation hypothesis, many-body localisation and other dynamical phase transitions, periodically-driven (Floquet) systems, adiabatic and counter-diabatic ramps, and spin-photon interactions. Moreover, QuSpin's user-friendly interface can easily be used in combination with other Python packages which makes it amenable to a high-level customisation. We explain how to use QuSpin using four detailed examples: (i) Standard exact diagonalisation of XXZ chain (ii) adiabatic ramping of parameters in the many-body localised XXZ model, (iii) heating in the periodically-driven transverse-field Ising model in a parallel field, and (iv) quantised light-atom interactions: recovering the periodically-driven atom in the semi-classical limit of a static Hamiltonian.
{"title":"QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains","authors":"P. Weinberg, Marin Bukov","doi":"10.21468/SciPostPhys.2.1.003","DOIUrl":"https://doi.org/10.21468/SciPostPhys.2.1.003","url":null,"abstract":"We present a new open-source Python package for exact diagonalization and quantum dynamics of spin(-photon) chains, called QuSpin, supporting the use of various symmetries in 1-dimension and (imaginary) time evolution for chains up to 32 sites in length. The package is well-suited to study, among others, quantum quenches at finite and infinite times, the Eigenstate Thermalisation hypothesis, many-body localisation and other dynamical phase transitions, periodically-driven (Floquet) systems, adiabatic and counter-diabatic ramps, and spin-photon interactions. Moreover, QuSpin's user-friendly interface can easily be used in combination with other Python packages which makes it amenable to a high-level customisation. We explain how to use QuSpin using four detailed examples: (i) Standard exact diagonalisation of XXZ chain (ii) adiabatic ramping of parameters in the many-body localised XXZ model, (iii) heating in the periodically-driven transverse-field Ising model in a parallel field, and (iv) quantised light-atom interactions: recovering the periodically-driven atom in the semi-classical limit of a static Hamiltonian.","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75293195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Lauricella, F. Cipolletta, G. Pontrelli, D. Pisignano, S. Succi
Electrospinning is a nanotechnology process whereby an external electric field is used to accelerate and stretch a charged polymer jet, so as to produce fibers with nanoscale diameters. In quest of a further reduction in the cross section of electrified jets hence of a better control on the morphology of the resulting electrospun fibers, we explore the effects of an external rotating electric field orthogonal to the jet direction. Through extensive particle simulations, it is shown that by a proper tuning of the electric field amplitude and frequency, a reduction of up to a $30 %$ in the aforementioned radius can be obtained, thereby opening new perspectives in the design of future ultra-thin electrospun fibres. Applications can be envisaged in the fields of nanophotonic components as well as for designing new and improved filtration materials.
{"title":"Effects of Orthogonal Rotating Electric Fields on Electrospinning Process","authors":"M. Lauricella, F. Cipolletta, G. Pontrelli, D. Pisignano, S. Succi","doi":"10.1063/1.4997086","DOIUrl":"https://doi.org/10.1063/1.4997086","url":null,"abstract":"Electrospinning is a nanotechnology process whereby an external electric field is used to accelerate and stretch a charged polymer jet, so as to produce fibers with nanoscale diameters. In quest of a further reduction in the cross section of electrified jets hence of a better control on the morphology of the resulting electrospun fibers, we explore the effects of an external rotating electric field orthogonal to the jet direction. Through extensive particle simulations, it is shown that by a proper tuning of the electric field amplitude and frequency, a reduction of up to a $30 %$ in the aforementioned radius can be obtained, thereby opening new perspectives in the design of future ultra-thin electrospun fibres. Applications can be envisaged in the fields of nanophotonic components as well as for designing new and improved filtration materials.","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84396323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The RMPCDMD software package performs hybrid Molecular Dynamics simulations, coupling Multiparticle Collision Dynamics to model the solvent and Molecular Dynamics to model suspended colloids, including hydrodynamics, thermal fluctuations, and chemically active solvent particles and catalytic colloids. The main usage of RMPCDMD is the simulation of chemically powered nanomotors, but other setups are considered: colloids in the presence of a thermal gradients or forced flows. RMPCDMD is developed in Fortran 2008 with OpenMP for multithreaded operation and uses the HDF5-based H5MD file format for storing data. RMPCDMD comes with documentation and a tutorial for the simulation of chemically powered nanomotors.
{"title":"RMPCDMD: Simulations of colloids with coarse-grained hydrodynamics, chemical reactions and external fields","authors":"P. Buyl, Mu-Jie Huang, Laurens Deprez","doi":"10.5334/jors.142","DOIUrl":"https://doi.org/10.5334/jors.142","url":null,"abstract":"The RMPCDMD software package performs hybrid Molecular Dynamics simulations, coupling Multiparticle Collision Dynamics to model the solvent and Molecular Dynamics to model suspended colloids, including hydrodynamics, thermal fluctuations, and chemically active solvent particles and catalytic colloids. The main usage of RMPCDMD is the simulation of chemically powered nanomotors, but other setups are considered: colloids in the presence of a thermal gradients or forced flows. RMPCDMD is developed in Fortran 2008 with OpenMP for multithreaded operation and uses the HDF5-based H5MD file format for storing data. RMPCDMD comes with documentation and a tutorial for the simulation of chemically powered nanomotors.","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77310745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yang He, Yajuan Sun, Ruili Zhang, Yulei Wang, Jian Liu, H. Qin
We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. Via expanding the phase space to include time $t$, we give a more general construction of volume-preserving methods that can be applied to systems with time-dependent electromagnetic fields. The newly derived methods provide numerical solutions with good accuracy and conservative properties over long time of simulation. Furthermore, because of the use of processing technique the high order methods are explicit, and cost less than the methods derived from standard compositions, thus are more efficient. The results are verified by the numerical experiments. Linear stability analysis of the methods show that the high order processed method allows larger time step size during integration.
{"title":"High order volume-preserving algorithms for relativistic charged particles in general electromagnetic fields","authors":"Yang He, Yajuan Sun, Ruili Zhang, Yulei Wang, Jian Liu, H. Qin","doi":"10.1063/1.4962677","DOIUrl":"https://doi.org/10.1063/1.4962677","url":null,"abstract":"We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. Via expanding the phase space to include time $t$, we give a more general construction of volume-preserving methods that can be applied to systems with time-dependent electromagnetic fields. The newly derived methods provide numerical solutions with good accuracy and conservative properties over long time of simulation. Furthermore, because of the use of processing technique the high order methods are explicit, and cost less than the methods derived from standard compositions, thus are more efficient. The results are verified by the numerical experiments. Linear stability analysis of the methods show that the high order processed method allows larger time step size during integration.","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91129919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we develop Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations by applying conforming finite element methods in space and splitting methods in time. For the spatial discretisation, the criteria for choosing finite element spaces are presented such that the semi-discrete system possesses a discrete non-canonical Poisson structure. We apply a Hamiltonian splitting method to the semi-discrete system in time, then the resulting algorithm is Poisson preserving and explicit. The conservative properties of the algorithm guarantee the efficient and accurate numerical simulation of the Vlasov-Maxwell equations over long-time.
{"title":"Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations","authors":"Yang He, Yajuan Sun, H. Qin, Jian Liu","doi":"10.1063/1.4962573","DOIUrl":"https://doi.org/10.1063/1.4962573","url":null,"abstract":"In this paper, we develop Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations by applying conforming finite element methods in space and splitting methods in time. For the spatial discretisation, the criteria for choosing finite element spaces are presented such that the semi-discrete system possesses a discrete non-canonical Poisson structure. We apply a Hamiltonian splitting method to the semi-discrete system in time, then the resulting algorithm is Poisson preserving and explicit. The conservative properties of the algorithm guarantee the efficient and accurate numerical simulation of the Vlasov-Maxwell equations over long-time.","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72725875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
It is a widely held view that analytical integration is more accurate than the numerical one. In some special cases, however, numerical integration can be more advantageous than analytical integration. In our paper we show this benefit for the case of electric potential and field computation of charged triangles and rectangles applied in the boundary element method (BEM). Analytical potential and field formulas are rather complicated (even in the simplest case of constant charge densities), they have usually large computation times, and at field points far from the elements they suffer from large rounding errors. On the other hand, Gaussian cubature, which is an efficient numerical integration method, yields simple and fast potential and field formulas that are very accurate far from the elements. The simplicity of the method is demonstrated by the physical picture: the triangles and rectangles with their continuous charge distributions are replaced by discrete point charges, whose simple potential and field formulas explain the higher accuracy and speed of this method. We implemented the Gaussian cubature method for the purpose of BEM computations both with CPU and GPU, and we compare its performance with two different analytical integration methods. The ten different Gaussian cubature formulas presented in our paper can be used for arbitrary high-precision and fast integrations over triangles and rectangles.
{"title":"Electric potential and field calculation of charged BEM triangles and rectangles by Gaussian cubature","authors":"F. Gluck, D. Hilk","doi":"10.2528/PIERB17011107","DOIUrl":"https://doi.org/10.2528/PIERB17011107","url":null,"abstract":"It is a widely held view that analytical integration is more accurate than the numerical one. In some special cases, however, numerical integration can be more advantageous than analytical integration. In our paper we show this benefit for the case of electric potential and field computation of charged triangles and rectangles applied in the boundary element method (BEM). Analytical potential and field formulas are rather complicated (even in the simplest case of constant charge densities), they have usually large computation times, and at field points far from the elements they suffer from large rounding errors. On the other hand, Gaussian cubature, which is an efficient numerical integration method, yields simple and fast potential and field formulas that are very accurate far from the elements. The simplicity of the method is demonstrated by the physical picture: the triangles and rectangles with their continuous charge distributions are replaced by discrete point charges, whose simple potential and field formulas explain the higher accuracy and speed of this method. We implemented the Gaussian cubature method for the purpose of BEM computations both with CPU and GPU, and we compare its performance with two different analytical integration methods. The ten different Gaussian cubature formulas presented in our paper can be used for arbitrary high-precision and fast integrations over triangles and rectangles.","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84774261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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