scholarly journals On a Helmholtz transmission problem in planar domains with corners

2018 ◽  
Vol 371 ◽  
pp. 315-332 ◽  
Author(s):  
Johan Helsing ◽  
Anders Karlsson
Keyword(s):  
Transmission Problem ◽  
Planar Domains ◽  
Domains With Corners

scholarly journals Classification of spectra of the Neumann–Poincaré operator on planar domains with corners by resonance

2017 ◽  
Vol 34 (4) ◽  
pp. 991-1011 ◽  
Author(s):  
Johan Helsing ◽  
Hyeonbae Kang ◽  
Mikyoung Lim
Keyword(s):  
Planar Domains ◽  
Domains With Corners

scholarly journals Lightning Solvers for Potential Flows

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 227
Author(s):  
Peter J. Baddoo
Keyword(s):  
Convergence Rates ◽  
Mathematical Basis ◽  
New Class ◽  
Planar Domains ◽  
Potential Flows ◽  
Rational Function Approximation ◽  
Novel Algorithms ◽  
High Degree ◽  
Domains With Corners ◽  
Steady Potential

We present a method for computing potential flows in planar domains. Our approach is based on a new class of techniques, known as “lightning solvers”, which exploit rational function approximation theory in order to achieve excellent convergence rates. The method is particularly suitable for flows in domains with corners where traditional numerical methods fail. We outline the mathematical basis for the method and establish the connection with potential flow theory. In particular, we apply the new solver to a range of classical problems including steady potential flows, vortex dynamics, and free-streamline flows. The solution method is extremely rapid and usually takes just a fraction of a second to converge to a high degree of accuracy. Numerical evaluations of the solutions are performed in a matter of microseconds and can be compressed further with novel algorithms.

scholarly journals On optimal estimates for the Laplace-Leray commutator in planar domains with corners

2011 ◽  
Vol 139 (05) ◽  
pp. 1691-1691 ◽  
Author(s):  
Elaine Cozzi ◽  
Robert L. Pego
Keyword(s):  
Planar Domains ◽  
Optimal Estimates ◽  
Domains With Corners

scholarly journals Spectral bounds for the Neumann-Poincaré operator on planar domains with corners

2014 ◽  
Vol 124 (1) ◽  
pp. 39-57 ◽  
Author(s):  
Karl-Mikael Perfekt ◽  
Mihai Putinar
Keyword(s):  
Planar Domains ◽  
Spectral Bounds ◽  
Domains With Corners

scholarly journals The Euler Equations in Planar Domains with Corners

2019 ◽  
Vol 234 (1) ◽  
pp. 57-79 ◽  
Author(s):  
Christophe Lacave ◽  
Andrej Zlatoš
Keyword(s):  
Euler Equations ◽  
Planar Domains ◽  
Domains With Corners

scholarly journals A Sinc Quadrature Method for the Double-Layer Integral Equation in Planar Domains with Corners

1998 ◽  
Vol 10 (3) ◽  
pp. 291-317 ◽  
Author(s):  
Rainer Kress ◽  
Ian H. Sloan ◽  
Frank Stenger
Keyword(s):  
Integral Equation ◽  
Double Layer ◽  
Quadrature Method ◽  
Planar Domains ◽  
Sinc Quadrature ◽  
Domains With Corners

scholarly journals Euler Equations on General Planar Domains

Annals of PDE ◽  
2021 ◽  
Vol 7 (2) ◽  
Author(s):  
Zonglin Han ◽  
Andrej Zlatoš
Keyword(s):  
Euler Equations ◽  
Planar Domains

scholarly journals Renormalised energies and renormalisable singular harmonic maps into a compact manifold on planar domains

2021 ◽  
Author(s):  
Antonin Monteil ◽  
Rémy Rodiac ◽  
Jean Van Schaftingen
Keyword(s):  
Compact Manifold ◽  
Harmonic Maps ◽  
Planar Domains
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