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FASP, short for Fast Auxiliary Space Precondition- ing is an open-source software written in C which is aimed for developing mathematically optimal iterative methods for solving discretized partial differential equations (PDEs). It mainly utilizes the methodology of Auxiliary Space Preconditioning (ASP) to construct efficient linear solvers.
PennSim is an oil and gas reservoir simulator developed for research purpose.
It uses a general compositional formulation for the all the fluids and has included both black oil models and equation of state (EOS) compositional model. ParPennSim is a parallel reservoir simulator based on PennSim. In 2015, ParPennSim was successfully implemented on the world’s No. 1 supercomputer (up to November 2015) Tianhe-2 to test several benchmark problems, which showed its robustness, efficiency and parallel scalability.
Presentation: A Unified Approach to the Design and Analysis of AMG
A general framework for the design and analysis of two-level AMG methods is presented. The approach is to find a basis for locally-the-best coarse space then glued them together using carefully designed linear extension maps to form a global coarse space. Such coarse spaces, constructed locally, satisfy global approximation property and by estimating the local Poincaré constants, we obtain sharp bounds on the convergence rate of the resulting two-level methods. To illustrate the use of the theoretical framework in practice, we prove the uniform convergence of the classical two level AMG method for finite element discretization of a jump coefficient problem and anisotropic problems on a shape regular mesh.
International Conference on Multigrid and Multiscale Methods in Computational Sciences, Bruchsal, Germany
Presentation: A Unified Approach to the Construction of Coarse Spaces and Convergence Analysis in AMG
A general framework for the design and analysis of two-level AMG methods is presented. The approach is to find a basis for locally-the-best coarse space then glued them together using carefully designed linear extension maps to form a global coarse space. Such coarse spaces, constructed locally, satisfy global approximation property and by estimating the local Poincaré constants, we obtain sharp bounds on the convergence rate of the resulting two-level methods. To illustrate the use of the theoretical framework in practice, we prove the uniform convergence of the classical two level AMG method for finite element discretization of a jump coefficient problem and anisotropic problems on a shape regular mesh.
Presentation: A Unified Theory for Classical and Aggregation Based AMG
A unified convergence theory for both classical AMG and aggregation based AMG is developed. The coarse space in this theory is defined by the sum of locally low frequency spaces. As an application, the two-level uniform convergence of classical AMG and unsmoothed aggregation AMG for finite element discretized Poisson equation on a shape regular mesh is proved using this theory.
ePoster Presentation: On Robust and Efficient Parallel Reservoir Simulation on Tianhe-2
A parallel reservoir simulator is developed and implemented on the world’s fastest supercomputer Tianhe-2. Several benchmark problems are tested to prove the robustness, efficiency and parallel scalability of the simulator.
Presentation: Algebraic Multigrid Method for Implicit Smoothed Particle Hydro-dynamics
The aggregation based Alegebraic multigrid (AMG) method is generalized to solve the large-scale linear system of equations discretized from implicit SPH. Auxiliary grid approach is used to improve the efficiency and reduce the computational complexity.
Presentation: A Smoothed Particle Hydrodynamics Model for Electrokinetic Flows
A numerical scheme based on smoothed particle hydrodynamics(SPH) for solving Poisson-Nernst-Planck equations are developed and a fasp AMG solver are developed for solving SPH discretized Poisson equation.
Thesis Title: Parallel Algorithms for Tensor Contractions
Several parallel algorithms are developed to accelerate the calculation of tensor contractions. MPI implementations are also given for the contractions between two 3rd-order tensors.
Title: The Application of Numerical Methods on Quantum Mechanics
Numerical methods, especially FDM and FEM, are applied to solve the Schrödinger equation to search and check some phenomena in Physics.