Multigrid Methods: Axiomatic Convergence Theory for Linear and Weakly Nonlinear Problems

by Steven M. Wise, Abner J Salgado, Calvin Wong

This book introduces the theory of multigrid methods for the fast numerical solution of linear and weakly nonlinear elliptic PDE. We use the finite element method to discretize the PDE problems, as this is the most natural choice, and the reader will get a thorough treatment of finite elements. No previous exposure to numerical discretization methods is assumed. All that is required of the reader is some knowledge of matrix theory. Coding the multigrid method is difficult. This book will help the reader build basic multigrid codes using easy-to-read sample Matlab codes. We use a matrix-based approach in the first part of the book, both as a way of presenting the theory in a natural way, and as a means for translating the theory into practical codes. The operators in the text and codes have the same names, which makes reading the sample codes simple, even if the reader has never coded. We deviate from the matrix-based approach only in the presentation of the nonlinear theory in the second part, which represents an area of current research. The book takes the reader from the basics and simple implementation issues all the way to the front lines of research.

260 pages, Paperback

Published December 4, 2025

About the author

Steven M. Wise was an American legal scholar who specialized in animal protection issues, primatology, and animal intelligence. He has taught animal rights law at Harvard Law School, Vermont Law School, John Marshall Law School, Lewis & Clark Law School, and Tufts University School of Veterinary Medicine. He is a former president of the Animal Legal Defense Fund, and founder and president of the Nonhuman Rights Project. The Yale Law Journal has called him "one of the pistons of the animal rights movement."

Wise is the author of An American Trilogy (2009), in which he tells the story of how a piece of land in Tar Heel, North Carolina, was first the home of Native Americans until they were driven into near-extinction, then a slave plantation, and finally the site of factory hog farms and the world's largest slaughterhouse. Though the Heavens May Fall (2005), recounts the 1772 trial in England of James Somersett, a black man rescued from a ship heading for the West Indies slave markets, which gave impetus to the movement to abolish slavery in Britain and the United States (see Somersett's Case). Drawing the Line (2002), which describes the relative intelligence of animals and human beings. And Rattling the Cage (2000), in which he argues that certain basic legal rights should be extended to chimpanzees and bonobos.

Wise received his undergraduate education at the College of William & Mary. While at William & Mary, Wise first became interested in politics through his involvement in the anti-Vietnam War movement. Wise was awarded his J.D from Boston University in 1976, and became a personal injury lawyer. He was inspired to move into the area of animal rights after reading Peter Singer's Animal Liberation (1975), often referred to as the bible of the animal liberation movement. A practicing animal protection attorney, he was president of the nonprofit Nonhuman Rights Project, where he directed its Nonhuman Rights Project, the purpose of which is to obtain basic common law rights for at least some nonhuman animals. He lived in Coral Springs, Florida.

Wise has taught “Animal Rights Jurisprudence” at the Vermont, Lewis and Clark, University of Miami, and St. Thomas Law Schools, and has taught “Animal Rights Law” at the Harvard Law School and John Marshall Law School. He was also working on a fifth book, which will be a memoir about the Nonhuman Rights Project.

He has authored numerous law review, encyclopedia, and popular articles. His work for the legal rights of nonhuman animals was highlighted on Dateline NBC and was the subject of the documentary, A Legal Person.

He regularly traveled the world lecturing on animal rights jurisprudence and the Nonhuman Rights Project, and was a frequent guest on television and radio discussing animal rights law and the Nonhuman Rights Project.