Singular Boundary Method for Heat Conduction in Layered Materials
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Boundary Particle Method with High-Order Trefftz Functions
Copyright © 2010 Tech Science Press CMC, vol.13, no.3, pp.201-217, 2010 Boundary Particle Method with High-Order Trefftz Functions Wen Chen1;2, Zhuo-Jia Fu1;3 and Qing-Hua Qin3 Abstract: This paper presents high-order Trefftz functions for some commonly used differential operators. These Trefftz functions are then used to construct boundary particle method for solving inhomogeneous problems with the boundary discretization only, i.e., no inner nodes and mesh are required in forming the final linear equation system. It should be mentioned that the presented Trefftz functions are nonsingular and avoids the singularity occurred in the fundamental solution and, in particular, have no problem-dependent parameter. Numerical experiments demonstrate the efficiency and accuracy of the present scheme in the solution of inhomogeneous problems. Keywords: High-order Trefftz functions, boundary particle method, inhomoge- neous problems, meshfree 1 Introduction Since the first paper on Trefftz method was presented by Trefftz (1926), its math- ematical theory was extensively studied by Herrera (1980) and many other re- searchers. In 1995 a special issue on Trefftz method, was published in the jour- nal of Advances in Engineering Software for celebrating its 70 years of develop- ment [Kamiya and Kita (1995)]. Qin (2000, 2005) presented an overview of the Trefftz finite element and its application in various engineering problems. The Trefftz method employs T-complete functions, which satisfies the governing dif- ferential operators and is widely applied to potential problems [Cheung, Jin and Zienkiewicz (1989)], two-dimensional elastic problems [Zielinski and Zienkiewicz (1985)], transient heat conduction [Jirousek and Qin (1996)], viscoelasticity prob- 1 Center for Numerical Simulation Software in Engineering and Sciences, Department of Engineer- ing Mechanics, Hohai University, Nanjing, Jiangsu, P.R.China 2 Corresponding author. -
Dear Colleagues
Contents Part 1: Plenary Lectures The expanding role of applications in the development and validation of CFD at NASA D. M. Schuster .......…………………………………………….....…………………..………. Thermodynamically consistent systems of hyperbolic equations S. K. Godunov ...................................................................................................................................... Part 2: Keynote Lectures A brief history of shock-fitting M.D. Salas …………………………………………………………………....…..…………. Understanding aerodynamics using computers M.M. Hafez ……….............…………………………………………………………...…..………. Part 3: High-Order Methods A unifying discontinuous CPR formulation for the Navier-Stokes equations on mixed grids Z.J. Wang, H. Gao, T. Haga ………………………………………………………………................. Assessment of the spectral volume method on inviscid and viscous flows O. Chikhaoui, J. Gressier, G. Grondin .........……………………………………..............…..…. .... Runge–Kutta Discontinuous Galerkin method for multi–phase compressible flows V. Perrier, E. Franquet ..........…………………………………………..........………………..……... Energy stable WENO schemes of arbitrary order N.K. Yamaleev, M.H. Carpenter ……………………………………………………….............…… Part 4: Two-Phase Flow A hybrid method for two-phase flow simulations K. Dorogan, J.-M. Hérard, J.-P. Minier ……………………………………………..................…… HLLC-type Riemann solver for the Baer-Nunziato equations of compressible two-phase flow S.A. Tokareva, E.F. Toro ………………………………………………………………...........…… Parallel direct simulation Monte Carlo of two-phase gas-droplet -
Numerische Untersuchung Der Akustischen Eigenschaften Von Trennenden Und flankierenden Bauteilen
Braunschweiger Schriften zur Mechanik Nr. 64-2008 Numerische Untersuchung der akustischen Eigenschaften von trennenden und flankierenden Bauteilen von Dirk Clasen Institut für Angewandte Mechanik Technische Universität Braunschweig Herausgegeben vom Mechanik-Zentrum der Technischen Universität Braunschweig Schriftleiter: Prof. Dr. rer. nat. H. Antes Institut für Angewandte Mechanik Postfach 3329 38023 Braunschweig Tel.: 0531 / 391-7101 Fax: 0531 / 391-5843 Von der Fakultät Architektur, Bauingenieurwesen und Umweltwissenschaften der Technischen Universität Carolo-Wilhelmina zu Braunschweig zur Erlangung des Grades eines Doktor-Ingenieur (Dr.-Ing.) genehmigte Dissertation Tag der Einreichung: 27.06.2007 Tag der Prüfung: 14.04.2008 Berichter: Prof. Dr.–Ing. S. Langer Prof. Dr.–Ing. O. von Estorff Copyright 2008 D. Clasen, Braunschweig BSM 64-2008 ISBN 978-3-920395-63-0 Alle Rechte, insbesondere der Übersetzung in fremde Sprachen, vorbehalten. Mit Genehmigung des Autors ist es gestattet, dieses Heft ganz oder teilweise zu vervielfältigen. Zusammenfassung Die Bevölkerung Deutschlands ist dem Lärm durch eine Vielzahl von Schallquellen ausgesetzt. Straßen, Schienenwege, Flugplätze, Gewerbeanlagen, Sportanlagen und nicht zuletzt Nachbarn führen häufig zu Lärmproblemen. Auf Grund dieser immer stärker werdenden Lärmbelastungen gewinnt die Berechnung der Schalldämmung zunehmend an Bedeutung. Dabei spielt die Erfas- sung von beliebigen geometrischen, bauphysikalischen und bauakustischen Randbedingungen ei- ne entscheidende Rolle. Oftmals wird der Nachweis -
Symmetric Boundary Knot Method
Symmetric boundary knot method W. Chen* Simula Research Laboratory, P. O. Box. 134, 1325 Lysaker, Norway E-mail: [email protected] (submitted 28 Sept. 2001, revised 25, Feb. 2002) Abstract The boundary knot method (BKM) is a recent boundary-type radial basis function (RBF) collocation scheme for general PDE’s. Like the method of fundamental solution (MFS), the RBF is employed to approximate the inhomogeneous terms via the dual reciprocity principle. Unlike the MFS, the method uses a non-singular general solution instead of a singular fundamental solution to evaluate the homogeneous solution so as to circumvent the controversial artificial boundary outside the physical domain. The BKM is meshfree, super-convergent, integration-free, very easy to learn and program. The original BKM, however, loses symmetricity in the presence of mixed boundary. In this study, by analogy with Fasshauer’s Hermite RBF interpolation, we developed a symmetric BKM scheme. The accuracy and efficiency of the symmetric BKM are also numerically validated in some 2-D and 3-D Helmholtz and diffusion-reaction problems under complicated geometries. Keyword: boundary knot method; radial basis function; meshfree; method of fundamental solution; dual reciprocity BEM; symmetricity * This research is supported by Norwegian Research Council. 1 1.Introduction In recent years much effort has been devoted to developing a variety of meshfree schemes for the numerical solution of partial differential equations (PDE’s). The driving force behind the scene is that the mesh-based methods such as the standard FEM and BEM often require prohibitive computational effort to mesh or remesh in handling high- dimensional, moving boundary, and complex-shaped boundary problems. -
A Self-Singularity-Capturing Scheme for Fractional Differential Equations
A Self-Singularity-Capturing Scheme for Fractional Differential Equations Jorge L. Suzukia,b and Mohsen Zayernouria,c aDepartment of Mechanical Engineering, Michigan State University, East Lansing, MI, USA bDepartment of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, MI, USA cDepartment of Probability and Statistics, Michigan State University, East Lansing, MI, USA ARTICLE HISTORY Compiled April 30, 2020 ABSTRACT We develop a two-stage computational framework for robust and accurate time- integration of multi-term linear/nonlinear fractional differential equations. In the first stage, we formulate a self-singularity-capturing scheme, given avail- able/observable data for diminutive time, experimentally obtained or sampled from an approximate numerical solution utilizing a fine grid nearby the initial time. The fractional differential equation provides the necessary knowledge/insight on how the hidden singularity can bridge between the initial and the subsequent short-time so- lution data. In the second stage, we utilize the multi-singular behavior of solution in a variety of numerical methods, without resorting to making any ad-hoc/uneducated guesses for the solution singularities. Particularly, we employed an implicit finite- difference method, where the captured singularities, in the first stage, are taken into account through some Lubich-like correction terms, leading to an accuracy of order O(∆t3−α). We show that this novel framework can control the error even in the presence of strong multi-singularities. -
J. Calderon-Sanchez
Universidad Polit´ecnicade Madrid Escuela T´ecnicaSuperior de Ingenieros Navales Programa de Doctorado en Ingenier´ıaNaval y Oce´anica Numerical studies of the sloshing phenomenon using the Smoothed Particle Hydrodynamics (SPH) method. Javier Calderon-Sanchez Supervisor: Daniel Duque Campayo January, 2020 `Nothing in life is to be feared, it is only to be understood. Now is the time to understand more, so that we may fear less.' Marie Curie i ii Tribunal designado por la Comisión de Doctorado de la Universidad Politécnica de Madrid, en su reunión del día...............de.............................de 20..... Presidente: Vocal: Vocal: Vocal: Secretario: Suplente: Suplente: Realizado el acto de defensa y lectura de la Tesis el día..........de........................de 20 ... en la E.T.S.I. /Facultad.................................................... Calificación .................................................. EL PRESIDENTE LOS VOCALES EL SECRETARIO iv Declaration I hereby declare that the contents presented in this dissertation are original and, to the best of my knowledge, they contain no material published by another person, or substantial proportions of material that have been submitted for any degree or other purposes, except where specific reference is made to the work of others. I certify that the intellectual content of this thesis is the product of my own work and that all the assistance received in preparing this thesis and sources have been acknowledged. Javier Calderon-Sanchez January, 2020 v vi Abstract The purpose of the present thesis is to increase the applicability of Smoothed Particle Hydro- dynamics (SPH) method to sloshing problems relevant in engineering. The thesis is structured around three main topics: theoretical improvements on SPH, imple- mentation of tools and physical models within the open-source software AQUAgpusph, and studies on 3-D geometries and application cases. -
Potential Problems by Singular Boundary Method Satisfying Moment Condition
Copyright © 2009 Tech Science Press CMES, vol.54, no.1, pp.65-85, 2009 Potential Problems by Singular Boundary Method Satisfying Moment Condition Wen Chen1;2, Zhuojia Fu1 and Xing Wei1 Abstract: This study investigates the singular boundary method (SBM), a novel boundary-type meshless method, in the numerical solution of potential problems. Our finding is that the SBM can not obtain the correct solution in some tested cases, in particular, in the cases whose solution includes a constant term. To rem- edy this drawback, this paper presents an improved SBM formulation which is a linear sum of the fundamental solution adding in a constant term. It is stressed that this SBM approximation with the additional constant term has to satisfy the so-called moment condition in order to guarantees the uniqueness of the solution. The efficiency and accuracy of the present SBM scheme are demonstrated through detailed comparisons with the exact solution, the method of fundamental solutions and the regularized meshless method. Keywords: Singular boundary method, fundamental solution, singularity at the origin, moment condition, potential problem 1 Introduction Without a need of harassing mesh generation in the traditional FEM [Zienkiewicz and Taylor (1991)] and BEM [Ong and Lim (2005)], meshless methods [Li and Liu (2002)] have attracted much attention in recent years. This study focuses on the boundary-type meshless numerical techniques, for instance, method of funda- mental solutions (MFS) [Chen, Golberg and Hon (1998); Cheng, Young and Tsai (2000); Fairweather and Karageorghis (1998); Karageorghis (1992); Liu (2008); Marin (2008,2010a,2010b); Poullikkas, Karageorghis and Georgiou (1998); Reut- skiy (2005); Smyrlis and Karageorghis (2001)], boundary knot method (BKM) by Chen and Tanaka (2002), boundary particle method [Chen and Fu (2009): Fu, Chen 1 Center for Numerical Simulation Software in Engineering and Sciences, Department of Engineer- ing Mechanics, College of Civil Engineering, Hohai University, Nanjing, Jiangsu, P.R.China 2 Corresponding author. -
Annual Report 2014
ANNUAL REPORT 2014 www.svf.stuba.sk Table of Content 2014 ANNUAL REPOrt of the Faculty of Civil Engineering Bratislava © Faculty of Civil Engineering, Slovak University of Technology in Bratislava, 2015 Authorized contributions from the departments Introduction translation by Dagmar Špildová, Slovak University of Technology in Bratislava, Faculty of Civil Engineering, Department of Languages Language consultant: Debra Gambrill JD, Slovak University of Technology in Bratislava, Faculty of Civil Engineering, Department of Languages Editor: Jozef Urbánek Layout: Ivan Pokrývka TABLE OF CONTENT Introduction .....................................................................................................5 Bodies of The Faculty ........................................................................................8 Departments Department of Concrete Structures and Bridges ..................................................14 Department of Transportation Engineering .........................................................22 Department of Theoretical Geodesy ...................................................................26 Department of Surveying ..................................................................................33 Department of Geotechnics ..............................................................................39 Department of Land and Water Resources Management ........................................45 Department of Hydraulic Engineering .................................................................53 Department -
Singular Boundary Method for Solving Plane Strain Elastostatic Problems
International Journal of Solids and Structures 48 (2011) 2549–2556 Contents lists available at ScienceDirect International Journal of Solids and Structures journal homepage: www.elsevier.com/locate/ijsolstr Singular boundary method for solving plane strain elastostatic problems ⇑ Yan Gu a,b, Wen Chen a,b, , Chuan-Zeng Zhang c a Center for Numerical Simulation Software in Engineering and Sciences, Department of Engineering Mechanics, Hohai University, Nanjing 210098, PR China b State Key Laboratory of Structural Analysis for Industrial Equipment, University of Technology, Dalian 116024, PR China c Department of Civil Engineering, University of Siegen, Paul-Bonatz-Str. 9-11, D-57076 Siegen, Germany article info abstract Article history: This study documents the first attempt to apply the singular boundary method (SBM), a novel boundary Received 15 December 2010 only collocation method, to two-dimensional (2D) elasticity problems. Unlike the method of fundamental Received in revised form 16 April 2011 solutions (MFS), the source points coincide with the collocation points on the physical boundary by using Available online 14 May 2011 an inverse interpolation technique to regularize the singularity of the fundamental solution of the equa- tion governing the problems of interest. Three benchmark elasticity problems are tested to demonstrate Keywords: the feasibility and accuracy of the proposed method through detailed comparisons with the MFS, bound- Singular boundary method ary element method (BEM), and finite element method (FEM). Collocation method Ó 2011 Elsevier Ltd. All rights reserved. Singularity Origin intensity factor Inverse interpolation technique Elasticity problem 1. Introduction Thus, over the past decade, some considerable effort was de- voted to eliminating the need for meshing. -
The Galerkin Finite Element Method for a Multi-Term Time-Fractional
Journal of Computational Physics 281 (2015) 825–843 Contents lists available at ScienceDirect Journal of Computational Physics www.elsevier.com/locate/jcp The Galerkin finite element method for a multi-term time-fractional diffusion equation ∗ Bangti Jin a, , Raytcho Lazarov b, Yikan Liu c, Zhi Zhou b a Department of Computer Science, University College London, Gower Street, London, WC1E 6BT, UK b Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA c Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153, Japan a r t i c l e i n f o a b s t r a c t Article history: We consider the initial/boundary value problem for a diffusion equation involving multiple Received 27 January 2014 time-fractional derivatives on a bounded convex polyhedral domain. We analyze a Received in revised form 22 October 2014 space semidiscrete scheme based on the standard Galerkin finite element method using Accepted 26 October 2014 continuous piecewise linear functions. Nearly optimal error estimates for both cases of Available online 30 October 2014 initial data and inhomogeneous term are derived, which cover both smooth and nonsmooth Keywords: data. Further we develop a fully discrete scheme based on a finite difference discretization Multi-term time-fractional diffusion of the time-fractional derivatives, and discuss its stability and error estimate. Extensive equation numerical experiments for one- and two-dimensional problems confirm the theoretical Finite element method convergence rates. Error estimate © 2014 The Authors. Published by Elsevier Inc. This is an open access article under the CC Semidiscrete scheme BY license (http://creativecommons.org/licenses/by/3.0/). -
Acoplamento De Métodos Sem Malha Para Análise De Meios Poroelásticos Saturados
ACOPLAMENTO DE MÉTODOS SEM MALHA PARA ANÁLISE DE MEIOS POROELÁSTICOS SATURADOS Daniela Silva Santurio Tese de Doutorado apresentada ao Programa de Pós-graduação em Engenharia Civil, COPPE, da Universidade Federal do Rio de Janeiro, como parte dos requisitos necessários à obtenção do título de Doutor em Engenharia Civil. Orientadores: José Cláudio de Faria Telles José Antônio Fontes Santiago Rio de Janeiro Março de 2021 ACOPLAMENTO DE MÉTODOS SEM MALHA PARA ANÁLISE DE MEIOS POROELÁSTICOS SATURADOS Daniela Silva Santurio TESE SUBMETIDA AO CORPO DOCENTE DO INSTITUTO ALBERTO LUIZ COIMBRA DE PÓS-GRADUAÇÃO E PESQUISA DE ENGENHARIA DA UNIVERSIDADE FEDERAL DO RIO DE JANEIRO COMO PARTE DOS REQUISITOS NECESSÁRIOS À OBTENÇÃO DO GRAU DE DOUTOR EM CIÊNCIAS EM ENGENHARIA CIVIL. Orientadores: José Claudio de Faria Telles José Antônio Fontes Santiago Aprovada por: Prof. José Claudio de Faria Telles Prof. José Antônio Fontes Santiago Prof. Carlos Friedrich Loeffler Neto Dr. Edmundo Guimarães de Araújo Costa Prof. Luiz Carlos Wrobel Profa. Raquel Jahara Lobosco Prof. Webe João Mansur RIO DE JANEIRO, RJ - BRASIL MARÇO DE 2021 Santurio, Daniela Silva Acoplamento de métodos sem malha para análise de meios poroelásticos saturados/ Daniela Silva Santurio. – Rio de Janeiro: UFRJ/COPPE, 2021 XII, 144 p.: il.; 29,7 cm. Orientadores: José Cláudio de Faria Telles José Antônio Fontes Santiago Tese (doutorado)–UFRJ/COPPE/Programa de Engenharia Civil, 2021 Referências Bibliográficas: p.107-117. 1. Meshless. 2. MLPG. 3. MSF. 4. DRM 5. Poroelasticidade. 6. Acoplamento iterativo I. Telles, José Claudio de Faria et al. II. Universidade Federal do Rio de Janeiro, COPPE, Programa de Engenharia Civil. III. -
Solving Partial Differential Equations by Taylor Meshless Method Jie Yang
Solving Partial Differential Equations by Taylor Meshless Method Jie Yang To cite this version: Jie Yang. Solving Partial Differential Equations by Taylor Meshless Method. Mechanics [physics]. Université de Lorraine, 2018. English. NNT : 2018LORR0032. tel-01810687 HAL Id: tel-01810687 https://tel.archives-ouvertes.fr/tel-01810687 Submitted on 8 Jun 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. AVERTISSEMENT Ce document est le fruit d'un long travail approuvé par le jury de soutenance et mis à disposition de l'ensemble de la communauté universitaire élargie. Il est soumis à la propriété intellectuelle de l'auteur. Ceci implique une obligation de citation et de référencement lors de l’utilisation de ce document. D'autre part, toute contrefaçon, plagiat, reproduction illicite encourt une poursuite pénale. Contact : [email protected] LIENS Code de la Propriété Intellectuelle. articles L 122. 4 Code de la Propriété Intellectuelle. articles L 335.2- L 335.10 http://www.cfcopies.com/V2/leg/leg_droi.php http://www.culture.gouv.fr/culture/infos-pratiques/droits/protection.htm Ecole Doctorale EMMA (Mécanique et énergétique) Thèse Présentée et soutenue publiquement pour l’obtention du titre de DOCTEUR DE L’UNIVERSITE DE LORRAINE par Jie YANG Solving Partial Differential Equations by Taylor Meshless Method Soutenue le 22 janvier 2018 Membres du jury: Rapporteurs: Prof.