The Experts below are selected from a list of 378795 Experts worldwide ranked by ideXlab platform
E. Suraud - One of the best experts on this subject based on the ideXlab platform.
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Weighted Particle Method for solving the Boltzmann equation
Physical review. C Nuclear physics, 1991Co-Authors: Mitsuru Tohyama, E. SuraudAbstract:We propose a new, deterministic Method of solution of the nuclear Boltzmann equation. In this weighted Particle Method,'' two-body collisions are treated by a master equation for an occupation probability of each numerical Particle. We apply the Method to the quadrupole motion of {sup 12}C. A comparison with usual stochastic Methods is made. Advantages and disadvantages of the weighted Particle Method are discussed.
Michael C. Hillman - One of the best experts on this subject based on the ideXlab platform.
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RKPM2D: an open-source implementation of nodally integrated reproducing kernel Particle Method for solving partial differential equations
Computational Particle Mechanics, 2019Co-Authors: Tsung-hui Huang, Haoyan Wei, Jiun-shyan Chen, Michael C. HillmanAbstract:We present an open-source software RKPM2D for solving PDEs under the reproducing kernel Particle Method (RKPM)-based meshfree computational framework. Compared to conventional mesh-based Methods, RKPM provides many attractive features, such as arbitrary order of continuity and discontinuity, relaxed tie between the quality of the discretization and the quality of approximation, simple h -adaptive refinement, and ability to embed physics-based enrichment functions, among others, which make RKPM promising for solving challenging engineering problems. The aim of the present software package is to support reproducible research and serve as an efficient test platform for further development of meshfree Methods. The RKPM2D software consists of a set of data structures and subroutines for discretizing two-dimensional domains, nodal representative domain creation by Voronoi diagram partitioning, boundary condition specification, reproducing kernel shape function generation, domain integrations with stabilization, a complete meshfree solver, and visualization tools for post-processing. In this paper, a brief overview that covers the key theoretical aspects of RKPM is given, such as the reproducing kernel approximation, weak form using Nitsche’s Method for boundary condition enforcement, various domain integration schemes (Gauss quadrature and stabilized nodal integration Methods), as well as the fully discrete equations. In addition, the computer implementation aspects employed in RKPM2D are discussed in detail. Benchmark problems solved by RKPM2D are presented to demonstrate the convergence, efficiency, and robustness of the RKPM implementation.
Tsung-hui Huang - One of the best experts on this subject based on the ideXlab platform.
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Level set topology optimization for design-dependent pressure loads using the reproducing kernel Particle Method
Structural and Multidisciplinary Optimization, 2020Co-Authors: Andreas Neofytou, Tsung-hui Huang, Jiun-shyan Chen, Renato Picelli, H. Alicia KimAbstract:This paper presents a level set topology optimization Method in combination with the reproducing kernel Particle Method (RKPM) for the design of structures subjected to design-dependent pressure loads. RKPM allows for arbitrary Particle placement in discretization and approximation of unknowns. This attractive property in combination with the implicit boundary representation given by the level set Method provides an effective framework to handle the design-dependent loads by moving the Particles on the pressure boundary without the need of remeshing or special numerical treatments. Moreover, the reproducing kernel (RK) smooth approximation allows for the Young’s modulus to be interpolated using the RK shape functions. This is another advantage of the proposed Method as it leads to a smooth Young’s modulus distribution for smooth boundary sensitivity calculation which yields a better convergence. Numerical results show good agreement with those in the literature.
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RKPM2D: an open-source implementation of nodally integrated reproducing kernel Particle Method for solving partial differential equations
Computational Particle Mechanics, 2019Co-Authors: Tsung-hui Huang, Haoyan Wei, Jiun-shyan Chen, Michael C. HillmanAbstract:We present an open-source software RKPM2D for solving PDEs under the reproducing kernel Particle Method (RKPM)-based meshfree computational framework. Compared to conventional mesh-based Methods, RKPM provides many attractive features, such as arbitrary order of continuity and discontinuity, relaxed tie between the quality of the discretization and the quality of approximation, simple h -adaptive refinement, and ability to embed physics-based enrichment functions, among others, which make RKPM promising for solving challenging engineering problems. The aim of the present software package is to support reproducible research and serve as an efficient test platform for further development of meshfree Methods. The RKPM2D software consists of a set of data structures and subroutines for discretizing two-dimensional domains, nodal representative domain creation by Voronoi diagram partitioning, boundary condition specification, reproducing kernel shape function generation, domain integrations with stabilization, a complete meshfree solver, and visualization tools for post-processing. In this paper, a brief overview that covers the key theoretical aspects of RKPM is given, such as the reproducing kernel approximation, weak form using Nitsche’s Method for boundary condition enforcement, various domain integration schemes (Gauss quadrature and stabilized nodal integration Methods), as well as the fully discrete equations. In addition, the computer implementation aspects employed in RKPM2D are discussed in detail. Benchmark problems solved by RKPM2D are presented to demonstrate the convergence, efficiency, and robustness of the RKPM implementation.
Hongkai Zhao - One of the best experts on this subject based on the ideXlab platform.
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a grid based Particle Method for solving partial differential equations on evolving surfaces and modeling high order geometrical motion
Journal of Computational Physics, 2011Co-Authors: Shingyu Leung, John Lowengrub, Hongkai ZhaoAbstract:We develop numerical Methods for solving partial differential equations (PDE) defined on an evolving interface represented by the grid based Particle Method (GBPM) recently proposed in [S. Leung, H.K. Zhao, A grid based Particle Method for moving interface problems, J. Comput. Phys. 228 (2009) 7706-7728]. In particular, we develop implicit time discretization Methods for the advection-diffusion equation where the time step is restricted solely by the advection part of the equation. We also generalize the GBPM to solve high order geometrical flows including surface diffusion and Willmore-type flows. The resulting algorithm can be easily implemented since the Method is based on meshless Particles quasi-uniformly sampled on the interface. Furthermore, without any computational mesh or triangulation defined on the interface, we do not require remeshing or reparametrization in the case of highly distorted motion or when there are topological changes. As an interesting application, we study locally inextensible flows governed by energy minimization. We introduce tension force via a Lagrange multiplier determined by the solution to a Helmholtz equation defined on the evolving interface. Extensive numerical examples are also given to demonstrate the efficiency of the proposed approach.
Mitsuru Tohyama - One of the best experts on this subject based on the ideXlab platform.
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Weighted Particle Method for solving the Boltzmann equation
Physical review. C Nuclear physics, 1991Co-Authors: Mitsuru Tohyama, E. SuraudAbstract:We propose a new, deterministic Method of solution of the nuclear Boltzmann equation. In this weighted Particle Method,'' two-body collisions are treated by a master equation for an occupation probability of each numerical Particle. We apply the Method to the quadrupole motion of {sup 12}C. A comparison with usual stochastic Methods is made. Advantages and disadvantages of the weighted Particle Method are discussed.