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arXiv 2022年

作者： Glusa, Christian D'Elia, Marta Capodaglio, Giacomo Gunzburger, Max Bochev, Pavel B. Center for Computing Research Sandia National Laboratories AlbuquerqueNM United States Data Science and Computing Group Sandia National Laboratories LivermoreCA United States Computational Physics and Methods Group Los Alamos National Laboratory Los AlamosNM United States Department of Scientific Computing Florida State University TallahasseeFL United States

We introduce a mathematically rigorous formulation for a nonlocal interface problem with jumps and propose an asymptotically compatible finite element discretization for the weak form of the interface problem. After proving the well-posedness of the weak form, we demonstrate that solutions to the nonlocal interface problem converge to the corresponding local counterpart when the nonlocal data are appropriately prescribed. Several numerical tests in one and two dimensions show the applicability of our technique, its numerical convergence to exact nonlocal solutions, its convergence to the local limit when the horizons vanish, and its robustness with respect to the patch test. Copyright © 2022, The Authors. All rights reserved.

关键词： Finite element method

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Dynamical Causal Modeling from a Quantum Dynamical Perspective

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AIP Conference Proceedings 2010年第1期1281卷 1954-1959页

作者： Emre Demiralp Metin Demiralp aDepartment of Psychology University of Michigan 1012 East Hall 530 Church Street Ann Arbor MI 48109‐1043 USA bİstanbul Technical University Informatics Institute Group for Science and Methods of Computing Maslak 34469 İstanbul Türkiye (Turkey)

Recent research suggests that any set of first order linear vector ODEs can be converted to a set of specific vector ODEs adhering to what we have called “Quantum Harmonical Form (QHF)”. QHF has been developed using a virtual quantum multi harmonic oscillator system where mass and force constants are considered to be time variant and the Hamiltonian is defined as a conic structure over positions and momenta to conserve the Hermiticity. As described in previous works, the conversion to QHF requires the matrix coefficient of the first set of ODEs to be a normal matrix. In this paper, this limitation is circumvented using a space extension approach expanding the potential applicability of this method. Overall, conversion to QHF allows the investigation of a set of ODEs using mathematical tools available to the investigation of the physical concepts underlying quantum harmonic oscillators. The utility of QHF in the context of dynamical systems and dynamical causal modeling in behavioral and cognitive neuroscience is briefly discussed.

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Towards distributed multiscale simulation of biological processes

Towards distributed multiscale simulation of biological proc...

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7th IEEE International Conference on e-science Workshops, escienceW 201

作者： Bernsdorf, Jörg Berti, Guntram Chopard, Bastien Hegewald, Jan Krafczyk, Manfred Wang, Dinan Lorenz, Eric Hoekstra, Alfons German Research School for Simulation Sciences RWTH Aachen University Aachen Germany Berti CMM Consulting Mathematical Methods Bonn Germany Scientific and Parallel Computing Group University of Geneva Geneva Switzerland Institute for Computational Modeling in Civil Engineering Technische Universität Braunschweig Brunswick Germany Meteorological Institute University of Bonn Bonn Germany Section Computational Science University of Amsterdam Amsterdam Netherlands

ISBN: (纸本)9780769545981

The understanding of biological processes, e.g. related to cardio-vascular disease and treatment, can significantly be improved by numerical simulation. In this paper, we present an approach for a multiscale simulation environment, applied for the prediction of in-stent re-stenos is. Our focus is on the coupling of distributed, heterogeneous hardware to take into account the different requirements of the coupled sub-systems concerning computing power. For such a concept, which is an extension of the standard multiscale computing approach, we want to apply the term Distributed Multiscale computing. © 2011 IEEE.

关键词： Stents

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Array Flattening Trenasformations via Superoperators on Difference, Unit and Shift Operators

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AIP Conference Proceedings 2011年第1期1389卷 1200-1203页

In this paper, we introduce a new approach for array flattening. We first establish a relationship between the general array element and a specifically chosen reference element by using unit, shift, forward and backward difference operators. Then, we define an array function by multiplying the forward and backward difference operators with a single scalar variable t. This variable is a perturbating agent since the produced array is equivalent to the original array when t is 1. We define the discrete counterparts of the Taylor series and Taylor formula with remainder in the form of expansion in t powers. We also define array flatness as this array function’s flatness with respect to t. Then the use of an affine transformation via a superoperator (first degree polynomial in the array function on the function operator and the variable operator) to create a new array function makes the flattening possible. This is done by appropriately choosing the super operator’s coefficient functions. The Taylor polynomial’s reciprocal is taken as the first degree term coefficient. The flattened array is obtained by setting t=1 after the flattening in t becomes complete.

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Symposium: Recent developments in numerical schemes for Hilbert space related issues in science and engineering

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AIP Conference Proceedings 2012年第1期1504卷 784-784页

作者： Metin Demiralp Istanbul Technical University Informatics Institute Group for Science and Methods of Computing Maslak 34469 Istanbul Turkey

Metin Demiralp; Symposium: Recent developments in numerical schemes for Hilbert space related issues in science and engineering, AIP Conference Proceedings, Vol

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Quantum Dynamics of Multi Harmonic Oscillators Described by Time Variant Conic Hamiltonian and their Use in Contemporary sciences

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AIP Conference Proceedings 2010年第1期1281卷

作者： Metin Demiralp İstanbul Technical University Informatics Institute Group for Science and Methods of Computing Maslak 34469 İstanbul Türkiye Turkey

This work focuses on the dynamics of a system of quantum multi harmonic oscillators whose Hamiltonian is conic in positions and momenta with time variant coefficients. While it is simple, this system is useful for modeling the dynamics of a number of systems in contemporary sciences where the equations governing spatial or temporal changes are described by sets of ODEs. The dynamical causal models used readily in neuroscience can be indirectly described by these systems. In this work, we want to show that it is possible to describe these systems using quantum wave function type entities and expectations if the dynamic of the system is related to a set of ODEs.

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RECOVERY TYPE A POSTERIORI ERROR ESTIMATION OF AN ADAPTIVE FINITE ELEMENT METHOD FOR CAHN-HILLIARD EQUATION

arXiv

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arXiv 2023年

作者： Chen, Yaoyao Huang, Yunqing Yi, Nianyu Yin, Peimeng School of Mathematics and Statistics Anhui Normal University Wuhu241000 China Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China Multiscale Methods and Dynamics Group Computer Science and Mathematics Division Oak Ridge National Laboratory Oak RidgeTN37831 United States

In this paper, we derive a novel recovery type a posteriori error estimation of the Crank-Nicolson finite element method for the Cahn-Hilliard equation. To achieve this, we employ both the elliptic reconstruction technique and a time reconstruction technique based on three time-level approximations, resulting in an optimal a posteriori error estimator. We propose a time-space adaptive algorithm that utilizes the derived a posteriori error estimator as error indicators. Numerical experiments are presented to validate the theoretical findings, including comparing with an adaptive finite element method based on a residual type a posteriori error estimator. © 2023, CC BY-NC-ND.

关键词： Recovery

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Towards Distributed Multiscale Simulation of Biological Processes

Towards Distributed Multiscale Simulation of Biological Proc...

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IEEE International Conference on E-science Workshops

作者： Jorg Bernsdorf Guntram Berti Bastien Chopard Jan Hegewald Manfred Krafczyk Dinan Wang Eric Lorenz Alfons Hoekstra German Research School for Simulation Sciences RWTH Aachen University Aachen Germany Consulting mathematical methods Berti CMM Bonn Germany Scientific and Parallel Computing Group University of Geneva Geneva Switzerland Institute for Computational Modeling in Civil Engineering Technische Universität Braunschweig Brunswick Germany Meteorological Institute University of Bonn Bonn Germany Section Computational Science University of Amsterdam Amsterdam Netherlands

关键词： Computational modeling Couplings Biological system modeling Numerical models Muscles Automata Drugs

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A scalable domain decomposition method for FEM discretizations of nonlocal equations of integrable and fractional type

arXiv

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arXiv 2023年

作者： Klar, Manuel Capodaglio, Giacomo D’Elia, Marta Glusa, Christian Gunzburger, Max Vollmann, Christian Department of Mathematics Universität Trier Trier54296 Germany Center for Computing Research Sandia National Laboratories AlbuquerqueNM87321 United States Computational Physics and Methods Group Los Alamos National Laboratory Los AlamosNM87545 United States Pasteur Labs BrooklynNY11205 United States Oden Institute for Computational Science and Engineering University of Texas Austin78712 United States

Nonlocal models allow for the description of phenomena which cannot be captured by classical partial differential equations. The availability of efficient solvers is one of the main concerns for the use of nonlocal models in real world engineering applications. We present a domain decomposition solver that is inspired by substructuring methods for classical local equations. In numerical experiments involving finite element discretizations of scalar and vectorial nonlocal equations of integrable and fractional type, we observe improvements in solution time of up to 14.6x compared to commonly used solver *** Codes 34B10, 65M60, 45P05, 45A99, 65R99 Copyright © 2023, The Authors. All rights reserved.

关键词： Domain decomposition methods

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Matrix Algebraic Infinite Product Representation for Generalized Hypergeometric Functions of Typep+1Fp

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Applied Numerical Analysis & Computational Mathematics 2005年第2期2卷

作者： Metin Demi̇ralp Sevda Üsküplü İstanbul Technical University Informatics Institute Group for Science and Methods of Computing Maslak 34469 İstanbul Turkey Phone: +90 212 285 7077 Fax: +90 212 285 7073

We present a novel representation for generalized hypergeometric functions of type p +1 F p which is in fact defined by an infinite series in nonnegative integer powers of its argument. We first construct a first order vector differential equation such that the unknown vector's coefficient is the sum of a constant matrix and a matrix premultiplied by the reciprocal of the independent variable whereas its first order derivative has unit matrix coefficient. An infinite process of factor extractions and power annihilations is employed yielding finally a vector differential equation that can be easily and analytically solved. Truncation of this scheme can be used to get approximations to hypergeometric functions of type p +1 F p . These functions have regular singularities at 0 and 1 values of the independent variable together with another regular singularity at infinity. Hence the factors are chosen to reflect the expected behavior of the functions at the singular point in a descending contribution order. Factorization is realized also for regular points. A simple, yet meaningful, implementation seems to give quite promising results. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

关键词： matrices, factorization

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