Computing the Dirichlet-to-Neumann map via an integral equation with the adjoint generalized Neumann kernel
Naqos, Samir Murid, Ali H.M. Nasser, Mohamed M. S. Yeak, Su Hoe
Naqos, Samir
Murid, Ali H.M.
Nasser, Mohamed M. S.
Yeak, Su Hoe
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2024-10-21
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Article
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Adjoint generalized Neumann kernel,Dirichlet-to-Neumann map,Integral equation,Laplace's equation,Riemann–Hilbert problem
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Samir Naqos, Ali H.M. Murid, Mohamed M.S. Nasser, Su Hoe Yeak, Computing the Dirichlet-to-Neumann map via an integral equation with the adjoint generalized Neumann kernel, Partial Differential Equations in Applied Mathematics, Volume 12, 2024, 100967, ISSN 2666-8181, https://doi.org/10.1016/j.padiff.2024.100967.
Abstract
A new numerical method for computing the Dirichlet-to-Neumann map for Laplace's equation in simply and multiply connected smooth domains is introduced. This method is based on an integral equation with the adjoint generalized Neumann kernel. Contrary to the classical approach which requires numerical differentiation in a post-processing step, our method allows computing the Dirichlet-to-Neumann map directly without the need of numerical differentiation in post-processing. The results of our numerical experiments demonstrate that the proposed method gives better accuracy and is more efficient than the classical approach for large problems with unbounded multiply connected domains. © 2024 The Authors
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Elsevier B.V.
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Partial Differential Equations in Applied Mathematics
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2666-8181