TY - JOUR
T1 - A transform-based technique for solving boundary value problems on convex planar domains
AU - Hulse, Jesse J.
AU - Lanzani, Loredana
AU - Llewellyn Smith, Stefan G.
AU - Luca, Elena
N1 - Publisher Copyright:
© The Author(s) 2024. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
PY - 2024/6/1
Y1 - 2024/6/1
N2 - A new technique is presented that can be used to solve mixed boundary value problems for Laplace’s equation and the complex Helmholtz equation in bounded convex planar domains. This work is an extension of Crowdy (2015, CMFT, 15, 655–687) where new transform-based techniques were developed for boundary value problems for Laplace’s equation in circular domains. The key ingredient of the method is the analysis of the so-called global relation, which provides a coupling of integral transforms of the given boundary data and of the unknown boundary values. Three problems which involve mixed boundary conditions are solved in detail, as well as numerically implemented, to illustrate how to apply the new approach.
AB - A new technique is presented that can be used to solve mixed boundary value problems for Laplace’s equation and the complex Helmholtz equation in bounded convex planar domains. This work is an extension of Crowdy (2015, CMFT, 15, 655–687) where new transform-based techniques were developed for boundary value problems for Laplace’s equation in circular domains. The key ingredient of the method is the analysis of the so-called global relation, which provides a coupling of integral transforms of the given boundary data and of the unknown boundary values. Three problems which involve mixed boundary conditions are solved in detail, as well as numerically implemented, to illustrate how to apply the new approach.
KW - harmonic function
KW - mixed boundary value problem
KW - transform quasi-pair
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U2 - 10.1093/imamat/hxae018
DO - 10.1093/imamat/hxae018
M3 - Article
AN - SCOPUS:85205779545
SN - 0272-4960
VL - 89
SP - 574
EP - 597
JO - IMA Journal of Applied Mathematics
JF - IMA Journal of Applied Mathematics
IS - 3
ER -