TY - JOUR
T1 - A Stabilized Separation of Variables Method for the Modified Biharmonic Equation
AU - Askham, T.
N1 - Funding Information:
T. Askham’s work was supported by the Office of the Assistant Secretary of Defense for Research and Engineering and AFOSR under NSSEFF Program Award FA9550-10-1-0180 and the Office of the Assistant Secretary of Defense for Research and Engineering and AFOSR under Award FA9550-15-1-0385.
Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2018/9/1
Y1 - 2018/9/1
N2 - The modified biharmonic equation is encountered in a variety of application areas, including streamfunction formulations of the Navier–Stokes equations. We develop a separation of variables representation for this equation in polar coordinates, for either the interior or exterior of a disk, and derive a new class of special functions which makes the approach stable. We discuss how these functions can be used in conjunction with fast algorithms to accelerate the solution of the modified biharmonic equation or the “bi-Helmholtz” equation in more complex geometries.
AB - The modified biharmonic equation is encountered in a variety of application areas, including streamfunction formulations of the Navier–Stokes equations. We develop a separation of variables representation for this equation in polar coordinates, for either the interior or exterior of a disk, and derive a new class of special functions which makes the approach stable. We discuss how these functions can be used in conjunction with fast algorithms to accelerate the solution of the modified biharmonic equation or the “bi-Helmholtz” equation in more complex geometries.
KW - Fast multipole method
KW - Integral equation
KW - Modified biharmonic equation
KW - Separation of variables
KW - Special functions
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U2 - 10.1007/s10915-018-0679-9
DO - 10.1007/s10915-018-0679-9
M3 - Article
AN - SCOPUS:85043366076
VL - 76
SP - 1674
EP - 1697
JO - Journal of Scientific Computing
JF - Journal of Scientific Computing
SN - 0885-7474
IS - 3
ER -