TY - JOUR
T1 - A penalty-regularization-operator splitting method for the numerical solution of a scalar Eikonal equation
AU - Caboussat, Alexandre
AU - GLOWINSKI, Roland
N1 - Publisher Copyright:
© 2015, Fudan University and Springer-Verlag Berlin Heidelberg.
PY - 2015/9/8
Y1 - 2015/9/8
N2 - In this article, we discuss a numerical method for the computation of the minimal and maximal solutions of a steady scalar Eikonal equation. This method relies on a penalty treatment of the nonlinearity, a biharmonic regularization of the resulting variational problem, and the time discretization by operator-splitting of an initial value problem associated with the Euler-Lagrange equations of the regularized variational problem. A low-order finite element discretization is advocated since it is well-suited to the low regularity of the solutions. Numerical experiments show that the method sketched above can capture efficiently the extremal solutions of various two-dimensional test problems and that it has also the ability of handling easily domains with curved boundaries.
AB - In this article, we discuss a numerical method for the computation of the minimal and maximal solutions of a steady scalar Eikonal equation. This method relies on a penalty treatment of the nonlinearity, a biharmonic regularization of the resulting variational problem, and the time discretization by operator-splitting of an initial value problem associated with the Euler-Lagrange equations of the regularized variational problem. A low-order finite element discretization is advocated since it is well-suited to the low regularity of the solutions. Numerical experiments show that the method sketched above can capture efficiently the extremal solutions of various two-dimensional test problems and that it has also the ability of handling easily domains with curved boundaries.
KW - Dynamical flow
KW - Eikonal equation
KW - Finite element methods
KW - Minimal and maximal solutions
KW - Operator splitting
KW - Penalization of equality constraints
KW - Regularization methods
UR - http://www.scopus.com/inward/record.url?scp=84938589256&partnerID=8YFLogxK
U2 - 10.1007/s11401-015-0930-8
DO - 10.1007/s11401-015-0930-8
M3 - Journal article
AN - SCOPUS:84938589256
SN - 0252-9599
VL - 36
SP - 659
EP - 688
JO - Chinese Annals of Mathematics. Series B
JF - Chinese Annals of Mathematics. Series B
IS - 5
ER -