Software & Scientific Applications

PLTMG

PLTMG is a package for solving elliptic partial differential equations in general regions of the plane. It is based on a family of continuous Lagrange triangular finite elements. PLTMG features options for adaptive h, p, and hp refinement, coarsening, and mesh moving. It also supports the Bank-Holst parallel adaptive meshing paradigm.

Contribution: I contributed to the design of data structure that supports elements of variable (high) degrees. I designed and implement p-refinement/unrefinement and automatic hp refinement/unrefinement. I also implemented mesh regularization for the Bank-Holst parallel adaptive meshing paradigm.

Related publications:

1. R. E. Bank and H. Nguyen, A parallel hp-adaptive finite element method, in Recent Advances in Scientific Computing and Applications, vol. 586 of Contemporary Mathematics, Amer. Math. Soc., Provi- dence, RI, 2013, pp. 23–33.
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2. R. E. Bank and H. Nguyen, Mesh regularization in Bank-Holst parallel hp-adaptive meshing, in Domain Decomposition Methods in Science and Engineering XX, R. Bank, M. Holst

3. R. E. Bank and H. Nguyen, hp-Adaptive Finite Elements Based on Derivative Recovery and Superconvergence, Computing and Visualization in Science, 14 (2011), pp 287-299.
   [link|PDF]

4. R. E. Bank and H. Nguyen, Domain decomposition and hp-adaptive finite elements, in Domain Decomposition Methods in Science and Engineering XIX, Y. Huang, R. Kornhuber, O. Widlund, and J. Xu, eds., vol. 78 of Lecture Notes in Computational Science and Engineering, 2011, Springer, pp. 3–13.
   [link|PDF]

5. Hieu Trung Nguyen, p-adaptive and automatic hp-adaptive finite element methods for elliptic partial differential equations, PhD Thesis, UC SanDiego, 2010.
   [link|PDF] A Software Package for Solving Elliptic Partial Differential Equations

IWFM: Integrated Water Flow Model

IWFM is a water resources management and planning model that simulates groundwater, surface water, stream-groundwater interaction, and other components of the hydrologic system. It is developed at Bay-Delta Office, Department of Water Resources, California, USA. Contribution: I worked with the nonlinear/linear solvers in the model. I formulated adaptive tolerances and adaptive damping to balance the cost of the inner and outer iterations of the Newton-GMRES method and achieved 26% speed up. Related publications: H. Nguyen and Z. Bai, E. Dogrul, T. Kadir, C. Brush, F. Chung, On Using the Newton-PGMRES Method for Multiscale Integrated Hydrologic Models. [PDF] H. Nguyen and Z. Bai, E. Dogrul, T. Kadir, C. Brush, F. Chung, Adaptive Accuracy Control of Nonlinear Newton-Krylov Methods for Multiscale Integrated Hydrologic Models, in XIX International Conference on Computational Methods in Water Resources, 2012. [link|PDF]

AWP-ODC: Anelastic Wave Propagation - K. Olsen, S. Day, Y. Cui

AWP-ODC is a highly scalable, parallel finite-difference application developed at SDSC and SDSU to simulate dynamic rupture and wave propagation that occurs during an earthquake.

Contribution: I improved the computation of the finite difference stencil in the bottle neck of the application using better mathematical formulation and more efficient data storage. The improvement yields 30% speed up.

Related publication

1. H. Nguyen, Yifeng Cui, Kim Olsen, Kwangyoon Lee , Single CPU optimizations of SCEC AWP-Olsen application, Poster, Southern California Earthquake Center Annual Meeting, 2009.
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deal.II: A Finite Element Differential Equations Analysis Library

deal.II is a C++ program library targeted at the computational solution of partial differential equations using adaptive finite elements. It uses state-of-the-art programming techniques to offer a modern interface to the complex data structures and algorithms required.

Currently, I am using the library and PETSc to implement domain decomposition and adaptivity for phase-field models in simulations of solidification and multiphase flow in porous media on pose-scale.