Title: On the Numerical Solution of Helmholtz's Equation by the Capacitance Matrix Method Classic Reprint
Publisher: Forgotten Books
Publication Date: 2018
Language: English
ISBN 10: 0484304496
ISBN 13: 9780484304498
Binding: HRD
Condition: New
Weight: 381 grams

About this title

Synopsis

Efficiently solve Helmholtz problems with a specialized matrix approach

Discover a fast, boundary-focused method for two-dimensional Helmholtz equations using the capacitance matrix framework. This edition highlights how a discretized problem can be transformed into a more tractable system that leverages specialized solvers and potential theory ideas.

The text explains how to model interior Dirichlet and Neumann problems on bounded regions, with emphasis on practical algorithmic choices. It discusses when and why to use a conjugate gradient method, how to manage matrix conditioning, and how to connect discrete approaches to classical potential theory for reliable results.

How to frame a bounded region and impose a uniform mesh for stability
Strategies for solving the resulting linear system efficiently
When a fast solver is advantageous and how the Woodbury formula relates to the approach
Impact of boundary conditions and problem setup on conditioning and convergence

Ideal for readers of applied mathematics and computational science who want a practical, solver-focused view of elliptic problems and their discrete counterparts. This edition is suitable for researchers, students, and professionals exploring specialized Helmholtz solvers and fast linear-algebra techniques.

"About this title" may belong to another edition of this title.

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