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A Parallel Two-Phase Flow Solver on Unstructured Mesh in 3D 23rd

A Parallel Two-Phase Flow Solver on Unstructured Mesh in 3D

引用

23rd International Conference on Domain Decomposition Methods

作者： Luo, Li Zhang, Qian Wang, Xiao-Ping Cai, Xiao-Chuan Hong Kong Univ Sci & Technol Dept Math Kowloon Hong Kong Peoples R China Shenzhen Inst Adv Technol Shenzhen Peoples R China Univ Colorado Dept Comp Sci Boulder CO 80309 USA

ISBN: (纸本)9783319523897;9783319523880

Two-phase flow problem plays an important role in many scientific and engineering processes. The problem can be described by a phase-field model consisting of the coupled Cahn-Hilliard and Navier-Stokes equations with the generalized Navier boundary condition. Accurate simulation of the interface and contact line motion requires very fine meshes, and the computation in 3D is even more challenging. Thus, the use of high performance computers and scalable parallel algorithms are indispensable. In this paper, we introduce a finite element method on unstructured 3D meshes with a semi-implicit time integration scheme, and a highly parallel solution strategy using different solvers for different components of the discretization. More precisely, we apply a restricted additive Schwarz preconditioned GMRES method to solve the systems arising from implicit discretization of the Cahn-Hilliard equation and the velocity equation, and an algebraic multigrid preconditioned CG method to solve the pressure Poisson system. Numerical experiments show that the strategy is efficient and scalable for 3D problems with complex geometry and on a supercomputer with a large number of processors. © Springer International Publishing AG 2017.

关键词： Two phase flow

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Adaptive BDDC Deluxe Methods for H(curl) 23rd

Adaptive BDDC Deluxe Methods for H(curl)

引用

23rd International Conference on Domain Decomposition Methods

作者： Zampini, Stefano King Abdullah Univ Sci & Technol Comp Elect & Math Sci & Engn Div Extreme Comp Res Ctr Thuwal Saudi Arabia

ISBN: (纸本)9783319523897;9783319523880

The work presents numerical results using adaptive BDDC deluxe methods for preconditioning the linear systems arising from finite element discretizations of the time-domain, quasi-static approximation of the Maxwell’s equations. The provided results, obtained using the BDDC implementation of the PETSc library, show that these methods are poly-logarithmic in the polynomial degree of the Nédélec elements of first and second kind, and robust with respect to arbitrary distributions of the magnetic permeability and the conductivity of the medium. © Springer International Publishing AG 2017.

关键词： Linear systems

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On the Discrete Maximum Principle for Algebraic Flux Correction Schemes with Limiters of Upwind Type 1

引用

Conference on Boundary and Interior Layers - computational and Asymptotic Methods (BAIL)

作者： Knobloch, Petr Charles Univ Prague Fac Math & Phys Dept Numer Math Sokolovska 83 Prague 18675 8 Czech Republic

ISBN: (数字)9783319672021

ISBN: (纸本)9783319672021;9783319672014

Algebraic flux correction (AFC) schemes are applied to the numerical solution of scalar steady-state convection- diffusion-reaction equations. A general result on the discrete maximum principle (DMP) is established under a weak assumption on the limiters and used for proving the DMP for a particular limiter of upwind type under an assumption that may hold also on non-Delaunay meshes. Moreover, a simple modification of this limiter is proposed that guarantees the validity of the DMP on arbitrary simplicial meshes. Furthermore, it is shown that AFC schemes do not provide sharp approximations of boundary layers if meshes do not respect the convection direction in an appropriate way.

关键词： Boundary layers

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An Adaptive Coarse Space for PL Lions Algorithm and Optimized Schwarz Methods 23rd

An Adaptive Coarse Space for PL Lions Algorithm and Optimize...

引用

23rd International Conference on Domain Decomposition Methods

作者： Haferssas, Ryadh Jolivet, Pierre Nataf, Frederic Lab Jacques Louis Lions Paris France Toulouse Inst Comp Sci Res Toulouse France

ISBN: (纸本)9783319523897;9783319523880

Optimized Schwarz methods (OSM) are very popular methods which were introduced in Lions (On the Schwarz alternating method. III: a variant for nonoverlapping subdomains. In: Chan TF, Glowinski R, Périaux J, Widlund O (eds) Third international symposium on domain decomposition methods for partial differential equations, Houston, TX, March 20-22, 1989. SIAM, Philadelphia, PA, 1990) for elliptic problems and in Després (C R Acad Sci Paris 1(6):313-316, 1990) for propagative wave phenomena. We build here a coarse space for which the convergence rate of the two-level method is guaranteed regardless of the regularity of the coefficients. We do this by introducing a symmetrized variant of the ORAS (Optimized Restricted Additive Schwarz) algorithm (St-Cyr et al., SIAM J Sci Comput 29(6):2402-2425 (electronic), 2007) and by identifying the problematic modes using two different generalized eigenvalue problems instead of only one as in Spillane et al. (C R Math Acad Sci Paris 351(5-6):197-201, 2013) and Spillane et al. (Numer Math 126(4):741-770, 2014) for the ASM (Additive Schwarz method), BDD [balancing domain decomposition (Mandel, Comm Appl Numer Methods 9:233-241, 1992)] or FETI [finite element tearing and interconnection (Farhat and Roux, Int J Numer Meth Eng 32:1205-1227, 1991)] methods. © Springer International Publishing AG 2017.

关键词： Domain decomposition methods

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Monotonic Convergence to Eigenvalues of Totally Nonnegative Matrices in an Integrable Variant of the Discrete Lotka-Volterra System 1st

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2nd International Workshop on Eigenvalue Problems - Algorithms, Software and Applications in Petascale Computing (EPASA)

作者： Tobita, Akihiko Fukuda, Akiko Ishiwata, Emiko Iwasaki, Masashi Nakamura, Yoshimasa Tokyo Univ Sci Grad Sch Sci Dept Math Sci Informat Sci Tokyo 1628601 Japan Shibaura Inst Technol Dept Math Sci Saitama 3378570 Japan Tokyo Univ Sci Dept Math Informat Sci Tokyo 1628601 Japan Kyoto Prefectural Univ Fac Life & Environm Sci Kyoto 6068522 Japan Kyoto Univ Grad Sch Informat Kyoto 6068501 Japan

ISBN: (纸本)9783319624266;9783319624242

The Lotka-Volterra (LV) system describes a simple predator-prey model in mathematical biology. The hungry Lotka-Volterra (hLV) system assumed that each predator preys on two or more species is an extension;those involving summations and products of nonlinear terms are referred to as summation-type and product-type hLV systems, respectively. Time-discretizations of these systems are considered in the study of integrable systems, and have been shown to be applicable to computing eigenvalues of totally nonnegative (TN) matrices. Monotonic convergence to eigenvalues of TN matrices, however, has not yet been observed in the time-discretization of the product-type hLV system. In this paper, we show the existence of a center manifold associated with the time-discretization of the product-type hLV system, and then clarify how the solutions approach an equilibrium corresponding to the eigenvalues of TN matrices in the final phase of convergence.

关键词： Eigenvalues and eigenfunctions

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On the Definition of Dirichlet and Neumann Conditions for the Biharmonic Equation and Its Impact on Associated Schwarz Methods 23rd

On the Definition of Dirichlet and Neumann Conditions for th...

引用

23rd International Conference on Domain Decomposition Methods

作者： Gander, Martin J. Liu, Yongxiang Univ Geneva Sect Math 2-4 Rue LievreCP 64 CH-1211 Geneva Switzerland China Acad Engn Phys Microsyst & Terahertz Res Ctr Chengdu 610200 Sichuan Peoples R China

ISBN: (纸本)9783319523897;9783319523880

The biharmonic equation is a fourth order equation, and thus needs two boundary conditions, and not just one like Laplace’s equation. While the clamped boundary condition can be taken naturally as the “Dirichlet” condition, there are also other choices, and we are interested in studying the dependence of Schwarz methods on the choice one makes for the “Dirichlet” condition when defining the Schwarz algorithm. We show that the classical choice actually leads to a very slow Schwarz algorithm and makes the biharmonic equation appear to be difficult to solve by Schwarz methods. A different choice for the “Dirichlet” condition leads to a much faster Schwarz algorithm comparable to the Schwarz algorithm applied to the Laplace equation. We then show that optimized Schwarz methods can automatically correct this problem, independently of what choice one makes for the “Dirichlet” condition, and they are in all cases largely superior to the classical Schwarz method. © Springer International Publishing AG 2017.

关键词： Boundary conditions

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Filter Diagonalization Method by Using a Polynomial of a Resolvent as the Filter for a Real Symmetric-Definite Generalized Eigenproblem 1

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2nd International Workshop on Eigenvalue Problems - Algorithms, Software and Applications in Petascale Computing (EPASA)

作者： Murakami, Hiroshi Tokyo Metropolitan Univ 1-1 Minami Osawa Hachioji Tokyo 1920397 Japan

ISBN: (数字)9783319624266

ISBN: (纸本)9783319624266;9783319624242

For a real symmetric-definite generalized eigenproblem of size N matrices Av = lambda Bv (B > 0), we solve those pairs whose eigenvalues are in a real interval [a, b] by the filter diagonalization method. In our present study, the filter which we use is a real-part of a polynomial of a resolvent: F = Re Sigma(n )(k=1)gamma(k){R(rho)}(k). Here R(rho) = (A - rho B)(-1) B is the resolvent with a non-real complex shift rho, and gamma(k) are coefficients. In our experiments, the (half) degree n is 15 or 20. By tuning the shift rho and coefficients {gamma(k)} well, the filter passes those eigenvectors well whose eigenvalues are in a neighbor of [a, b], but strongly reduces those ones whose eigenvalues are separated from the interval. We apply the filter to a set of sufficiently many B-orthonormal random vectors {x((l))}to obtain another set {y((l))}. From both sets of vectors and properties of the filter, we construct a basis which approximately spans an invariant subspace whose eigenvalues are in a neighbor of [a, b]. An application of the Rayleigh-Ritz procedure to the basis gives approximations of all required eigenpairs. Experiments for banded problems showed this approach worked in success.

关键词： Eigenvalues and eigenfunctions

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Direct and Iterative Methods for Numerical Homogenization 23rd

Direct and Iterative Methods for Numerical Homogenization

引用

23rd International Conference on Domain Decomposition Methods

作者： Kornhuber, Ralf Podlesny, Joscha Yserentant, Harry FU Berlin Berlin Germany TU Berlin Berlin Germany

ISBN: (纸本)9783319523897;9783319523880

Elliptic problems with oscillating coefficients can be approximated up to arbitrary accuracy by using sufficiently fine meshes, i.e., by resolving the fine scale. Well-known multiscale finite elements (Henning et al. ESAIM: Math. Model. Numer. Anal. 48:1331-1349, 2014;Målqvist and Peterseim, Math. Comput. 83:2583-2603, 2014) can be regarded as direct numerical homogenization methods in the sense that they provide approximations of the corresponding (unfeasibly) large linear systems by much smaller systems while preserving the fine-grid discretization accuracy (model reduction). As an alternative, we present iterative numerical homogenization methods that provide approximations up to fine-grid discretization accuracy and discuss differences and commonalities. © Springer International Publishing AG 2017.

关键词： Homogenization method

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A DG Least-Squares Finite Element Method for Nagumo's Nerve Equation with Fast Reaction: A Numerical Study 1

引用

Conference on Boundary and Interior Layers - computational and Asymptotic Methods (BAIL)

作者： Lin, Runchang Texas A&M Int Univ Dept Math & Phys Laredo TX 78041 USA

ISBN: (数字)9783319672021

ISBN: (纸本)9783319672021;9783319672014

The Nagumo equation is a simple nonlinear reaction-diffusion equation, which has important applications in neuroscience and biological electricity. If the equation is reaction-dominated, numerical oscillationsmay appear near the traveling wave front, which makes it challenging to find stable solutions. In the present study, a new method is developed on uniform meshes to solve the Nagumo equation. Numerical results are given to demonstrate the performance of the algorithm. Convergence rates with respect to spatial and temporal discretization are obtained experimentally. Some properties of the nerve model are confirmed numerically.

关键词： Numerical methods

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Properties of Definite Bethe-Salpeter Eigenvalue Problems 1

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2nd International Workshop on Eigenvalue Problems - Algorithms, Software and Applications in Petascale Computing (EPASA)

作者： Shao, Meiyue Yang, Chao Lawrence Berkeley Natl Lab Berkeley CA 94720 USA

ISBN: (数字)9783319624266

ISBN: (纸本)9783319624266;9783319624242

The Bethe-Salpeter eigenvalue problem is solved in condense matter physics to estimate the absorption spectrum of solids. It is a structured eigenvalue problem. Its special structure appears in other approaches for studying electron excitation in molecules or solids also. When the Bethe-Salpeter Hamiltonian matrix is definite, the corresponding eigenvalue problem can be reduced to a symmetric eigenvalue problem. However, its special structure leads to a number of interesting spectral properties. We describe these properties that are crucial for developing efficient and reliable numerical algorithms for solving this class of problems.

关键词： Eigenvalues and eigenfunctions

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