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Numerical approximation of one phase quadrature domains
Author(s) -
Bazarganzadeh Mahmoudreza,
Bozorgnia Farid
Publication year - 2013
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21773
Subject(s) - mathematics , solver , quadrature (astronomy) , nyström method , numerical analysis , boundary (topology) , partial differential equation , iterative method , domain (mathematical analysis) , boundary value problem , work (physics) , partial derivative , mathematical analysis , mathematical optimization , engineering , mechanical engineering , electrical engineering
In this work, we present two numerical schemes for a free boundary problem that is called one phase quadrature domain. In the first method, using the properties of a given free boundary problem, we derive a method that leads us to a fast iterative solver. The iteration procedure is adapted to work in the case when topology changes. The second method is based on shape reconstruction to establish an efficient shape Quasi‐Newton method. Various numerical experiments confirm the efficiency of the derived numerical methods. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013