128 citations · 346 across the 59 of their papers we have counts for
67 papers
Solution of a system of Hamilton-Jacobi equations on a network
Emily R. Hammett, Maria Teresa Chiri, Kenneth D. Czuprynski +1
We extend the study of Hamilton-Jacobi equations on networks from a single equation to a weakly coupled system of two equations on a star graph, and we develop a numerical scheme f…
A Conjugate Gradient Formulation of the EnKF Algorithm
Sanghyun Lee, Zhengqi Liu, Jonathan Valyou +1
Ensemble Kalman Filter (EnKF) based data assimilation algorithms synthesize predictive numerical forecast models with accumulated data as time evolves and account for model uncerta…
Improving accuracy of finite element solutions by smoothing
Yuwen Li, Han Shui, Ludmil Zikatanov
This paper develops a smoothing-based postprocessing method for improving the accuracy of finite element solutions. The method applies a few smoothing iterations, such as damped Ja…
A Mollification Approach to Ramified Transport and Tree Shape Optimization
Alberto Bressan, Giacomo Vecchiato, Ludmil Zikatanov
The paper analyzes a mollification algorithm, for the numerical computation of optimal irrigation patterns. This provides a regularization of the standard irrigation cost functiona…
Oscillation-free numerical schemes for Biot's model and their iterative coupling solution
Álvaro Pé de la Riva, Francisco J. Gaspar, Xiaozhe Hu +3
In this work, we present a new stabilization method aimed at removing spurious oscillations in the pressure approximation of Biot's model for poroelasticity with low permeabilities…
Reduced Krylov Basis Methods for Parametric Partial Differential Equations
Yuwen Li, Ludmil T. Zikatanov, Cheng Zuo
This work is on a user-friendly reduced basis method for solving a family of parametric PDEs by preconditioned Krylov subspace methods including the conjugate gradient method, gene…
A Local Fourier Analysis for Additive Schwarz Smoothers
Álvaro Pé de la Riva, Carmen Rodrigo, Francisco J. Gaspar +3
In this work, a local Fourier analysis is presented to study the convergence of multigrid methods based on additive Schwarz smoothers. This analysis is presented as a general frame…
Weakly coupled systems of eikonal equations for autonomous vehicles
Maria Teresa Chiri, Kenneth D Czuprynski, Ludmil T Zikatanov
In this paper, we study solutions for a weakly coupled system of eikonal equations arising in an optimal path-planning problem with random breakdown. The model considered takes int…
A reduced conjugate gradient basis method for fractional diffusion
Yuwen Li, Ludmil T. Zikatanov, Cheng Zuo
This work is on a fast and accurate reduced basis method for solving discretized fractional elliptic partial differential equations (PDEs) of the form by rationa…
Algebraic multigrid methods for metric-perturbed coupled problems
Ana Budisa, Xiaozhe Hu, Miroslav Kuchta +2
We develop multilevel methods for interface-driven multiphysics problems that can be coupled across dimensions and where complexity and strength of the interface coupling deteriora…
Parameter-free preconditioning for nearly-incompressible linear elasticity
James H Adler, Xiaozhe Hu, Yuwen Li +1
It is well known that via the augmented Lagrangian method, one can solve Stokes' system by solving the nearly incompressible linear elasticity equation. In this paper, we show that…
HAZniCS -- Software Components for Multiphysics Problems
Ana Budisa, Xiaozhe Hu, Miroslav Kuchta +2
We introduce the software toolbox HAZniCS for solving interface-coupled multiphysics problems. HAZniCS is a suite of modules that combines the well-known FEniCS framework for finit…
Rational approximation preconditioners for multiphysics problems
Ana Budisa, Xiaozhe Hu, Miroslav Kuchta +2
We consider a class of mathematical models describing multiphysics phenomena interacting through interfaces. On such interfaces, the traces of the fields lie (approximately) in the…
New stabilized finite element methods for nearly inviscid and incompressible flows
Yuwen Li, Ludmil Zikatanov
This work proposes a new stabilized finite element method for solving the incompressible Navier--Stokes equations. The numerical scheme is based on a reduced Bernar…
Neural networks with trainable matrix activation functions
Zhengqi Liu, Shuhao Cao, Yuwen Li +1
The training process of neural networks usually optimize weights and bias parameters of linear transformations, while nonlinear activation functions are pre-specified and fixed. Th…
A finite-element framework for a mimetic finite-difference discretization of Maxwell's equations
James H. Adler, Casey Cavanaugh, Xiaozhe Hu +1
Maxwell's equations are a system of partial differential equations that govern the laws of electromagnetic induction. We study a mimetic finite-difference (MFD) discretization of t…
Fast auxiliary space preconditioners on surfaces
Yuwen Li
This work presents uniform preconditioners for the discrete Laplace--Beltrami operator on hypersurfaces. In particular, within the framework of fast auxiliary space preconditioning…
Nodal auxiliary a posteriori error estimates
Yuwen Li, Ludmil T. Zikatanov
We introduce and explain key relations between a posteriori error estimates and subspace correction methods viewed as preconditioners for problems in infinite dimensional Hilbert s…
A Posteriori Error Estimates for Solving Graph Laplacians
Xiaozhe Hu, Kaiyi Wu, Ludmil T. Zikatanov
In this paper, we study a posteriori error estimators which aid multilevel iterative solvers for linear systems with graph Laplacians. In earlier works such estimates were computed…
On the unisolvence for the quasi-polynomial spaces of differential forms
Shuonan Wu, Ludmil T. Zikatanov
We consider quasi-polynomial spaces of differential forms defined as weighted (with a positive weight) spaces of differential forms with polynomial coefficients. We show that the u…
A posteriori error estimates of finite element methods by preconditioning
Yuwen Li, Ludmil Zikatanov
We present a framework that relates preconditioning with a posteriori error estimates in finite element methods. In particular, we use standard tools in subspace correction methods…
Discrete Trace Theorems and Energy Minimizing Spring Embeddings of Planar Graphs
John C. Urschel, Ludmil T. Zikatanov
Tutte's spring embedding theorem states that, for a three-connected planar graph, if the outer face of the graph is fixed as the complement of some convex region in the plane, and…
Automatic coarsening in Algebraic Multigrid utilizing quality measures for matching-based aggregations
Pasqua D'Ambra, Fabio Durastante, Salvatore Filippone +1
In this paper, we discuss the convergence of an Algebraic MultiGrid (AMG) method for general symmetric positive-definite matrices. The method relies on an aggregation algorithm, na…
Residual-based a posteriori error estimates of mixed methods for a three-field Biot's consolidation model
Yuwen Li, Ludmil T. Zikatanov
We present residual-based a posteriori error estimates of mixed finite element methods for the three-field formulation of Biot's consolidation model. The error estimator is an uppe…