Discover practical, math‑driven techniques for solving boundary value problems with the capacitance matrix approach. This book presents finite element methods for the Helmholtz and Poisson equations, focusing on stable triangulations, discretization choices, and efficient computation. It blends theory with algorithms you can implement, from mesh construction to solver strategies.

Written for engineers and scientists who design and analyze numerical solvers, the text explains how to build and work with the stiffness and mass matrices, manage boundary conditions, and apply embedding and domain decomposition ideas in a finite element setting. It also covers both linear and quadratic elements and discusses how to leverage fast solvers and multigrid techniques to handle large systems.

How triangulation quality impacts convergence and how to generate robust meshes.

Construction and interpretation of the finite element system with stiffness and mass matrices.

Different boundary treatments (Neumann and Dirichlet) and their effect on solvers.

Strategies for fast computation, including FFT‑based methods and multigrid cycles.

Ideal for readers engaged in numerical PDEs, computational electromagnetics, or advanced finite element methods who seek a solid, implementable framework.

About the Author

Christoph Borgers has been a Professor in the Department of Mathematics at Tufts University since 1994. He has also worked at the University of Michigan and at the IBM T. J. Watson Research Center. He received his PhD from New York University.

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