TITLE:
Patchwise Mapping Method for Solving Elliptic Boundary Value Problems Containing Multiple Singularities
AUTHORS:
Hyunju Kim
KEYWORDS:
Mapping Method, Non-Uniform Rational B-Spline (NURBS), Galerkin Approximation, Isogeometric Analysis, Multiple Singularities
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.7,
July
29,
2019
ABSTRACT: In the paper [1], the geometrical mapping techniques based on Non-Uniform Rational B-Spline (NURBS) were introduced to solve an elliptic boundary value problem containing a singularity. In the mapping techniques, the inverse function of the NURBS geometrical mapping generates singular functions as well as smooth functions by an unconventional choice of control points. It means that the push-forward of the NURBS geometrical mapping that generates singular functions, becomes a piecewise smooth function. However, the mapping method proposed is not able to catch singularities emerging at multiple locations in a domain. Thus, we design the geometrical mapping that generates singular functions for each singular zone in the physical domain. In the design of the geometrical mapping, we should consider the design of control points on the interface between/among patches so that global basis functions are in C0space. Also, we modify the B-spline functions whose supports include the interface between/among them. We put the idea in practice by solving elliptic boundary value problems containing multiple singularities.