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05/10/2023
Algebraic multigrid methods for metric-perturbed coupled problems
We develop multilevel methods for interface-driven multiphysics problems...
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03/31/2023
Parameter-free preconditioning for nearly-incompressible linear elasticity
It is well known that via the augmented Lagrangian method, one can solve...
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10/24/2022
HAZniCS – Software Components for Multiphysics Problems
We introduce the software toolbox HAZniCS for solving interface-coupled ...
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10/20/2022
Structure-Preserving Discretization of Fractional Vector Calculus using Discrete Exterior Calculus
Fractional vector calculus is the building block of the fractional parti...
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09/23/2022
Rational approximation preconditioners for multiphysics problems
We consider a class of mathematical models describing multiphysics pheno...
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08/27/2022
Pressure-robust enriched Galerkin methods for the Stokes equations
In this paper, we present a pressure-robust enriched Galerkin (EG) schem...
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08/08/2022
A Stable Mimetic Finite-Difference Method for Convection-Dominated Diffusion Equations
Convection-diffusion equations arise in a variety of applications such a...
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07/21/2022
A Deep Neural Network/Meshfree Method for Solving Dynamic Two-phase Interface Problems
In this paper, a meshfree method using the deep neural network (DNN) app...
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07/16/2022
Solving Graph Laplacians via Multilevel Sparsifiers
We consider effective preconditioners for solving Laplacians of general ...
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06/07/2022
Effective Preconditioners for Mixed-Dimensional Scalar Elliptic Problems
Discretization of flow in fractured porous media commonly lead to large ...
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03/29/2022
A Multigrid Preconditioner for Spatially Adaptive High-order Meshless Method on Fluid-solid Interaction Problems
We present a monolithic geometric multigrid preconditioner for solving f...
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10/11/2021
An Enriched Galerkin Method for the Stokes Equations
We present a new enriched Galerkin (EG) scheme for the Stokes equations ...
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09/10/2021
An Efficient High-order Numerical Solver for Diffusion Equations with Strong Anisotropy
In this paper, we present an interior penalty discontinuous Galerkin fin...
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07/08/2021
Monolithic multigrid for a reduced-quadrature discretization of poroelasticity
Advanced finite-element discretizations and preconditioners for models o...
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06/25/2021
Ladder Polynomial Neural Networks
Polynomial functions have plenty of useful analytical properties, but th...
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12/22/2020
Enforcing exact physics in scientific machine learning: a data-driven exterior calculus on graphs
As traditional machine learning tools are increasingly applied to scienc...
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12/05/2020
A finite-element framework for a mimetic finite-difference discretization of Maxwell's equations
Maxwell's equations are a system of partial differential equations that ...
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07/01/2020
A Posteriori Error Estimates for Multilevel Methods for Graph Laplacians
In this paper, we study a posteriori error estimators which aid multilev...
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06/30/2020
Momentum Accelerated Multigrid Methods
In this paper, we propose two momentum accelerated MG cycles. The main i...
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06/18/2020
Well-posedness, discretization and preconditioners for a class of models for mixed-dimensional problems with high dimensional gap
In this work, we illustrate the underlying mathematical structure of mix...
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06/11/2020
Randomized Fast Subspace Descent Methods
Randomized Fast Subspace Descent (RFASD) Methods are developed and analy...
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05/11/2020
A Mesh-free Method Using Piecewise Deep Neural Network for Elliptic Interface Problems
In this paper, we propose a novel mesh-free numerical method for solving...
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03/07/2020
Diffusion State Distances: Multitemporal Analysis, Fast Algorithms, and Applications to Biological Networks
Data-dependent metrics are powerful tools for learning the underlying st...
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10/10/2019
Mixed-Dimensional Auxiliary Space Preconditioners
This work introduces nodal auxiliary space preconditioners for discretiz...
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06/19/2019
Modifying AMG coarse spaces with weak approximation property to exhibit approximation in energy norm
Algebraic multigrid (AMG) coarse spaces are commonly constructed so that...
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08/20/2018