Related papers: The inverse fast multipole method: using a fast ap…
The novel contribution of this paper relies in the proposal of a fully implicit numerical method designed for nonlinear degenerate parabolic equations, in its convergence/stability analysis, and in the study of the related computational…
This paper provides a theoretical framework on the solution of feedforward ReLU networks for interpolations, in terms of what is called an interpolation matrix, which is the summary, extension and generalization of our three preceding…
This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some output variables are also input variables, linked by a linear dependency. Fundamental examples include the…
This paper proposes a new method for estimating sparse precision matrices in the high dimensional setting. It has been popular to study fast computation and adaptive procedures for this problem. We propose a novel approach, called Sparse…
We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this…
Boundary value problems involving elliptic PDEs such as the Laplace and the Helmholtz equations are ubiquitous in mathematical physics and engineering. Many such problems can be alternatively formulated as integral equations that are…
As a follow up to \cite{Causley2013}, we provide a detailed description of the numerical implementation of an O(N), A-stable, second order accurate solution of the wave equation, constructed from semi-discrete boundary value problems. We…
This note proposes an efficient preconditioner for solving linear and semi-linear parabolic equations. With the Crank-Nicholson time stepping method, the algebraic system of equations at each time step is solved with the conjugate gradient…
The efficient solution of moderately large-scale linear systems arising from the KKT conditions in optimal control problems (OCPs) is a critical challenge in robotics. With the stagnation of Moore's law, there is growing interest in…
This paper presents our work on developing parallel computational methods for two-phase flow on modern parallel computers, where techniques for linear solvers and nonlinear methods are studied and the standard and inexact Newton methods are…
Sparse direct linear solvers are at the computational core of domain decomposition preconditioners and therefore have a strong impact on their performance. In this paper, we consider the Fast and Robust Overlapping Schwarz (FROSch) solver…
A technique for computing an ILU preconditioner based on the FAPINV algorithm is presented. We show that this algorithm is well-defined for H-matrices. Moreover, when used in conjunction with Krylov-subspace-based iterative solvers such as…
This paper introduces a sparse matrix discrete interpolation method to effectively compute matrix approximations in the reduced order modeling framework. The sparse algorithm developed herein relies on the discrete empirical interpolation…
Modeling multiphysics processes in porous media requires preconditioned iterative linear solvers to enable efficient simulations at industry-relevant scales. These solvers are typically composed of sub-algorithms that target individual…
Neural PDE solvers offer a powerful tool for modeling complex dynamical systems, but often struggle with error accumulation over long time horizons and maintaining stability and physical consistency. We introduce a multiscale implicit…
Model predictive control (MPC) for linear dynamical systems requires solving an optimal control structured quadratic program (QP) at each sampling instant. This paper proposes a primal active-set strategy (PRESAS) for the efficient solution…
We present an improved algorithm for solving symmetrically diagonally dominant linear systems. On input of an $n\times n$ symmetric diagonally dominant matrix $A$ with $m$ non-zero entries and a vector $b$ such that $A\bar{x} = b$ for some…
The solution of linear systems of equations is a central task in a number of scientific and engineering applications. In many cases the solution of linear systems may take most of the simulation time thus representing a major bottleneck in…
Large sparse symmetric linear systems appear in several branches of science and engineering thanks to the widespread use of the finite element method (FEM). The fastest sparse linear solvers available implement hybrid iterative methods.…
In this paper we propose and analyze new efficient sparse approximate inverse (SPAI) smoothers for solving the two-dimensional (2D) and three-dimensional (3D) Laplacian linear system with geometric multigrid methods. Local Fourier analysis…