https://doi.org/10.26089/NumMet.v27r324

Boundary Element Method for 2D capacitances calculation in extraction problems

Authors

  • Vasiliy V. Sazonov
  • Mikhail M. Khapaev

Keywords:

extraction
capacitance matrix
boundary element method

Abstract

The paper considers two-dimensional problems of calculating the electrostatic capacitance matrix that arise in mathematical modeling of microelectronic structures using equivalent circuits with lumped parameters at the stage of physical verification (the extraction problem). Such problems have a number of features, including the complex structure of dielectrics and conductors and the necessity of correct data generation for mass computations. For a numerical solution, the boundary element method is used, which is based on the representation of the solution as a potential of a simple layer. Two modern implementations of this well-known approach are considered, based on application of the simple Galerkin method and the non-standard collocation method both supplemented by a priori generated adapted computational mesh. A comparison of the convergence, accuracy and performance of these algorithms is carried out. The Galerkin method is more accurate for systems of equations with a matrix of moderate dimension, whereas the collocation procedure is faster in the case of matrices of large dimensions. Both algorithms are quite efficient and can be used as an integral part of extraction computational algorithms. Additional problems related to the calculation of a capacitance matrix are discussed, including the modeling of floating conductors and the calculating capacitance derivatives by geometric and other parameters.


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Published

2026-07-14

Issue

Vol. 27 (2026): Issue 3.

Section

Methods and algorithms of computational mathematics and their applications

Authors

Vasiliy V. Sazonov

Lomonosov Moscow State University, Faculty of Space Research

• Dean

Mikhail M. Khapaev

Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

• Associate Professor

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Copyright (c) 2026 В. В. Сазонов, М. М. Хапаев

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