TY - JOUR
T1 - Geometric solution strategy of Laplace problems with free boundary
AU - Poutala, Arto
AU - Tarhasaari, Timo
AU - Kettunen, Lauri
PY - 2016/3/9
Y1 - 2016/3/9
N2 - This paper introduces a geometric solution strategy for Laplace problems. Our main interest and emphasis is on efficient solution of the inverse problem with a boundary with Cauchy condition and with a free boundary. This type of problem is known to be sensitive to small errors. We start from the standard Laplace problem and establish the geometric solution strategy on the idea of deforming equipotential layers continuously along the field lines from one layer to another. This results in exploiting ordinary differential equations to solve any boundary value problem that belongs to the class of Laplace's problem. Interpretation in terms of a geometric flow will provide us with stability considerations. The approach is demonstrated with several examples.
AB - This paper introduces a geometric solution strategy for Laplace problems. Our main interest and emphasis is on efficient solution of the inverse problem with a boundary with Cauchy condition and with a free boundary. This type of problem is known to be sensitive to small errors. We start from the standard Laplace problem and establish the geometric solution strategy on the idea of deforming equipotential layers continuously along the field lines from one layer to another. This results in exploiting ordinary differential equations to solve any boundary value problem that belongs to the class of Laplace's problem. Interpretation in terms of a geometric flow will provide us with stability considerations. The approach is demonstrated with several examples.
KW - Bernoulli problem
KW - Cauchy condition
KW - Differential equations
KW - Elliptic partial differential equations
KW - Equipotential layers
KW - Field lines
KW - Inverse problem
KW - Laplace problem
KW - Mean curvature
KW - Shape design
U2 - 10.1002/nme.4988
DO - 10.1002/nme.4988
M3 - Article
VL - 105
SP - 723
EP - 746
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
IS - 10
ER -