27 citations · 35 across the 7 of their papers we have counts for
8 papers
A nonoverlapping spectral additive Schwarz method for interior penalty discontinuous Galerkin discretizations of Anisotropic Elliptic Problems
Maurice S. Fabien, Sijing Liu, Marcus Sarkis
We design and analyze a nonoverlapping additive Schwarz preconditioner for interior penalty discontinuous Galerkin discretizations of anisotropic elliptic problems. The preconditio…
Low-order divergence-free approximations for the Stokes problem on Worsey-Farin and Powell-Sabin splits
Maurice Fabien, Johnny Guzman, Michael Neilan +1
We derive low-order, inf-sup stable and divergence-free finite element approximations for the Stokes problem using Worsey-Farin splits in three dimensions and Powell-Sabin splits i…
Hybridization and postprocessing in finite element exterior calculus
Gerard Awanou, Maurice Fabien, Johnny Guzmán +1
We hybridize the methods of finite element exterior calculus for the Hodge-Laplace problem on differential -forms in . In the cases and , we recover…
A high order hybridizable discontinuous Galerkin method for incompressible miscible displacement in heterogeneous media
Maurice S. Fabien, Matthew G. Knepley, Beatrice M. Riviere
We present a new method for approximating solutions to the incompressible miscible displacement problem in porous media. At the discrete level, the coupled nonlinear system has bee…
Comparative study of finite element methods using the Time-Accuracy-Size (TAS) spectrum analysis
Justin Chang, Maurice S. Fabien, Matthew G. Knepley +1
We present a performance analysis appropriate for comparing algorithms using different numerical discretizations. By taking into account the total time-to-solution, numerical accur…
A hybridizable discontinuous Galerkin method for two-phase flow in heterogeneous porous media
Maurice S. Fabien, Matthew G. Knepley, Beatrice M. Riviere
We present a new method for simulating incompressible immiscible two-phase flow in porous media. The semi-implicit method decouples the wetting phase pressure and saturation equati…
Manycore parallel computing for a hybridizable discontinuous Galerkin nested multigrid method
M. S. Fabien, M. G. Knepley, R. T. Mills +1
We present a parallel computing strategy for a hybridizable discontinuous Galerkin (HDG) nested geometric multigrid (GMG) solver. Parallel GMG solvers require a combination of coar…
A Radial Basis Function (RBF) Method for the Fully Nonlinear 1D Serre Green-Naghdi Equations
Maurice S. Fabien
In this paper, we present a spectral method based on Radial Basis Functions (RBFs) for numerically solving the fully nonlinear 1D Serre Green-Naghdi equations. The approximation us…