In this review we describe a transient type of gas discharge which is commonly called a
streamer discharge, as well as a few related phenomena in pulsed discharges. Streamers …

Jacobian-free Newton–Krylov (JFNK) methods are synergistic combinations of Newton-type
methods for superlinearly convergent solution of nonlinear equations and Krylov subspace …

Machine learning develops rapidly, which has made many theoretical breakthroughs and is
widely applied in various fields. Optimization, as an important part of machine learning, has …

U-Nets are a go-to neural architecture across numerous tasks for continuous signals on a
square such as images and Partial Differential Equations (PDE), however their design and …

We present a general-purpose solver for convex quadratic programs based on the
alternating direction method of multipliers, employing a novel operator splitting technique …

The purpose of this text is to offer an overview of the most popular domain decomposition
methods for partial differential equations (PDEs). The presentation is kept as much as …

This book gives an introduction to the finite element method as a general computational
method for solving partial differential equations approximately. Our approach is …

Excerpt More than 25 years have passed since the first edition of this book was published in
1996. Least squares and least-norm problems have become more significant with every …

The mathematical theory of Krylov subspace methods with a focus on solving systems of
linear algebraic equations is given a detailed treatment in this principles-based book …

Large linear systems of saddle point type arise in a wide variety of applications throughout
computational science and engineering. Due to their indefiniteness and often poor spectral …