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检索条件"丛书名=Lecture Notes in Computational Science and Engineering 37"

共 864 条记录，以下是51-60 订阅

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A Data-Driven Multiscale Theory for Modeling Damage and Fracture of Composite Materials 9th

A Data-Driven Multiscale Theory for Modeling Damage and Frac...

引用

9th International Workshop on Meshfree Methods for Partial Differential Equations

作者： Shakoor, Modesar Gao, Jiaying Liu, Zeliang Liu, Wing Kam Northwestern Univ Dept Mech Engn Evanston IL 60208 USA Livermore Software Technol Corp LSTC Livermore CA USA

ISBN: (纸本)9783030151195;9783030151188

The advent of advanced processing andmanufacturing techniques has led to newmaterial classes with complexmicrostructures across scales from nanometers to meters. In this paper, a data-driven computational framework for the analysis of these complex material systems is presented. A mechanistic concurrent multiscale method called Self-consistent Clustering Analysis (SCA) is developed for general inelastic heterogeneous material systems. The efficiency of SCA is achieved via data compression algorithms which group local microstructures into clusters during the training stage, thereby reducing required computational expense. Its accuracy is guaranteed by introducing a self-consistent method for solving the Lippmann-Schwinger integral equation in the prediction stage. The proposed framework is illustrated for a composite cutting process where fracture can be analyzed simultaneously at the microstructure and part scales.

关键词： Microstructure

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Stable and Efficient Quantum Mechanical Calculations with PUMA on Triclinic Lattices 9th

Stable and Efficient Quantum Mechanical Calculations with PU...

引用

9th International Workshop on Meshfree Methods for Partial Differential Equations

作者： Albrecht, Clelia Klaar, Constanze Schweitzer, Marc Alexander Fraunhofer Inst Algorithmen & Wissensch Rechnen S St Augustin Germany Rhein Friedrich Wilhelms Univ Bonn Inst Numer Simulat Bonn Germany

ISBN: (纸本)9783030151195;9783030151188

In this paper we are concerned with the efficient approximation of the Schrodinger eigenproblem using an orbital-enriched flat-top partition of unity method on general triclinic cells. To this end, we generalize the approach presented in Albrecht et al. (Comput. Meth. Appl. Mech. Eng. 342:224-239, 2018) via a simple yet effective transformation approach and discuss its realization in the PUMA software framework. The presented results clearly show that the proposed scheme attains all convergence and stability properties presented in Albrecht et al.

关键词： Stability

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Fluid Structure Interaction (FSI) in the MESHFREE Finite Pointset Method (FPM): Theory and Applications 9th

Fluid Structure Interaction (FSI) in the MESHFREE Finite Poi...

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9th International Workshop on Meshfree Methods for Partial Differential Equations

作者： Kuhnert, Jorg Michel, Isabel Mack, Reiner Fraunhofer Inst Ind Math ITWM Kaiserslautern Germany Voith Hydro Holding GmbH & Co KG Heidenheim Germany

ISBN: (纸本)9783030151195;9783030151188

Fluid Structure Interaction ( FSI) and meshfree numerical methods are a perfect couple. One often repeated strong argument is the almost natural coupling of meshfree methods in a Lagrangian/ALE formulation with moving, flexible structures. Since 1996, Fraunhofer ITWM has been developing a Generalized Finite Difference Method (GFDM), a purelymeshfree solver for fluid and continuum mechanics. In the industrial context, this method is also referred to as Finite Pointset Method (FPM). Currently, it is further developed to an integrated tool called MESHFREE which combines the advantages of GFDM/FPM as well as SAMG, a fast solver for large sparse linear systems developed by Fraunhofer SCAI. This synergy drastically increases the applicability of themethod since SAMG provides a robust and scalable linear solver for a wide class of problems. In this contribution, we classify fundamental FSI aspects in GFDM/FPM: classical pressure-velocity coupling and alternative velocity-pressure coupling. Each category will be illustrated by industrially relevant examples, with special focus on Pelton turbine applications and flow in flexible tubes.

关键词： Fluid structure interaction

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Kernel-Based Reconstructions for Parametric PDEs 9th

Kernel-Based Reconstructions for Parametric PDEs

引用

9th International Workshop on Meshfree Methods for Partial Differential Equations

作者： Kempf, Rudiger Wendland, Holger Rieger, Christian Univ Bayreuth Dept Math Appl & Numer Anal Bayreuth Germany Inst Numer Simulat Bonn Germany

ISBN: (纸本)9783030151195;9783030151188

In uncertainty quantification, an unknown quantity has to be reconstructed which depends typically on the solution of a partial differential equation. This partial differential equation itself may depend on parameters, some of them may be deterministic and some are random. To approximate the unknown quantity one therefore has to solve the partial differential equation (usually numerically) for several instances of the parameters and then reconstruct the quantity from these simulations. As the number of parameters may be large, this becomes a highdimensional reconstruction problem. We will address the topic of reconstructing such unknown quantities using kernel-based reconstruction methods on sparse grids. First, we will introduce into the topic, then explain the reconstruction process and finally provide new error estimates.

关键词： Partial differential equations

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Global-Local Enrichments in PUMA 9th

Global-Local Enrichments in PUMA

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9th International Workshop on Meshfree Methods for Partial Differential Equations

作者： Birner, Matthias Schweitzer, Marc Alexander Fraunhofer Inst Algorithmen & Wissensch Rechnen S St Augustin Germany Rhein Friedrich Wilhelms Univ Bonn Inst Numer Simulat Bonn Germany

ISBN: (纸本)9783030151195;9783030151188

In this paper we present the global-local enrichment approach in a general partition of unity method. Moreover, we propose an automatic scheme of computing an optimal parameter in Robin boundary conditions for the local problem. We present results of two dimensional fracture mechanics problems to demonstrate the properties and performance of the resulting method.

关键词： Fracture mechanics

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Numerical Study of the RBF-FD Level Set Based Method for Partial Differential Equations on Evolving-in-Time Surfaces 9th

Numerical Study of the RBF-FD Level Set Based Method for Par...

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9th International Workshop on Meshfree Methods for Partial Differential Equations

作者： Sokolov, Andriy Davydov, Oleg Turek, Stefan TU Dortmund Inst Appl Math Dortmund Germany Univ Giessen Dept Math Giessen Germany

ISBN: (纸本)9783030151195;9783030151188

In this article we present a Radial Basis Function (RBF)-Finite Difference (FD) level set based method for the numerical solution of partial differential equations (PDEs) of the reaction-diffusion-convection type on an evolving-in-time hypersurface Gamma(t). In a series of numerical experiments we study the accuracy and robustness of the proposed scheme and demonstrate that the method is applicable to practical models.

关键词： Partial differential equations

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Parallel Detection of Subsystems in Linear Systems Arising in the MESHFREE Finite Pointset Method 9th

Parallel Detection of Subsystems in Linear Systems Arising i...

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9th International Workshop on Meshfree Methods for Partial Differential Equations

作者： Nick, Fabian Plum, Hans-Joachim Kuhnert, Jorg Fraunhofer SCAI St Augustin Germany Fraunhofer ITWM Kaiserslautern Germany

ISBN: (纸本)9783030151195;9783030151188

The Finite Pointset Method (FPM) is a meshfree method for simulations in the field of fluid dynamics and continuum mechanics (Tiwari and Kuhnert, Finite pointset method based on the projection method for simulations of the incompressible Navier-Stokes equations. Springer, Berlin, 2003). The key idea in FPM is to discretize the necessary differential operators by using stencils generated by a least squares approach on a pointcloud that is moving in every time step. Applying Algebraic Multigrid Methods (AMG) to the linear systems arising in FPM comes with various challenges, see our previous work Metsch et al. (Comput Vis Sci, reviewed) and Nick et al. (Linear solvers for the finite pointset method. In: Schafer, M., Behr, M., Mehl, M., Wohlmuth, B. (eds.) Recent advances in computational engineering. Springer, Cham, 2018). In Nick et al. (Linear solvers for the finite pointset method. In: Schafer, M., Behr, M., Mehl, M., Wohlmuth, B. (eds.) Recent advances in computational engineering. Springer, Cham, 2018) we limited ourselves to essentially irreducible matrices, saying that if a matrix arising from FPM is not essentially irreducible, we can employ a parallel algorithm in order to detect those subsystems that are essentially irreducible. This paper introduces the algorithm that we use in order to detect independent parts of the FPM pointcloud, which we call components. The algorithm that we propose has a theoretical complexity of O(vertical bar V vertical bar) in the average case, where vertical bar V vertical bar is the number of points in the pointcloud. Our experiments with a real world model however show that in practice the complexity is much better. The experiments also show that in order to guarantee a stable convergence of the arising linear systems, detecting components is essential, as singular components can occur in certain situations.

关键词： Linear systems

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Modeling the Friction Drilling Process Using a Thermo-Mechanical Coupled Smoothed Particle Galerkin Method 9th

Modeling the Friction Drilling Process Using a Thermo-Mechan...

引用

9th International Workshop on Meshfree Methods for Partial Differential Equations

作者： Wu, Cheng-Tang Wu, Youcai Hu, Wei Pan, Xiaofei Livermore Software Technol Corp Livermore CA 94551 USA

ISBN: (纸本)9783030151195;9783030151188

This paper presents an up-to-date Lagrangian particle method for the analysis of a coupled thermo-mechanical problem in the friction drilling simulation. The method is obtained by a modification of variational equations using the penalized approach to avoid onerous stability problems in conventional Lagrangian particle methods and to obtain semi-discrete equations that are amenable to temporal and spatial integration using the staggered explicit time marching scheme. To deal with the critical numerical limitation associated with large deformation and material separation at the bushing forming stage, the method is furnished with an adaptive anisotropic Lagrangian kernel and a bond-based failure criterion. Representative simulation of a thermal-mechanical coupled friction drilling process is studied, and results are comparedwith the experimental data to examine the validity of this study.

关键词： Galerkin methods

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A Fast and Stable Multi-Level Solution Technique for the Method of Fundamental Solutions 9th

A Fast and Stable Multi-Level Solution Technique for the Met...

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9th International Workshop on Meshfree Methods for Partial Differential Equations

作者： Gaspar, Csaba Szechenyi Istvan Univ Gyor Hungary

ISBN: (纸本)9783030151195;9783030151188

The classical form of the Method of Fundamental Solutions is applied. Instead of using a single set of subtly located external sources, a special strategy of defining several sets of external source points is introduced. The sets of sources are defined by the quadtree/octtree subdivision technique controlled by the boundary collocation points in a completely automatic way, resulting in a point set, the density of the spatial distribution of which decreases quickly far from the boundary. The 'far' sources are interpreted to form a 'coarse grid', while the densely distributed 'near-boundary' sources are considered a 'fine grid' (despite they need not to have any grid structure). Based on this classification, a multi- level technique is built up, where the smoothing procedure is defined by performing some familiar iterative technique e.g. the (conjugate) gradient method. The approximate solutions are calculated by enforcing the boundary conditions in the sense of least squares. The resulting multi-level method is robust and significantly reduces the computational cost. No weakly or strongly singular integrals have to be evaluated. Moreover, the problem of severely ill-conditioned matrices is completely avoided.

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Preconditioned Conjugate Gradient Solvers for the Generalized Finite Element Method 9th

Preconditioned Conjugate Gradient Solvers for the Generalize...

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9th International Workshop on Meshfree Methods for Partial Differential Equations

作者： Fillmore, Travis B. Gupta, Varun Duarte, Carlos Armando Univ Illinois Dept Civil & Environm Engn Urbana IL 61801 USA Pacific Northwest Natl Lab Richland WA 99352 USA

ISBN: (纸本)9783030151195;9783030151188

This paper focuses on preconditioners for the conjugate gradient method and their applications to the Generalized FEM with global-local enrichments (GFEM(gl)) and the Stable GFEM(gl). The preconditioners take advantage of the hierarchical struture of the matrices in these methods and the fact that most of the matrix does not change when simulating for example, the evolution of interfaces and fractures. The performance of the conjugate gradient method with the proposed preconditioner is investigated. A 3-D fracture problem is adopted for the numerical experiments.

关键词： Conjugate gradient method

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