Null Field and Interior Field Methods for Laplace’s Equation in Circular Domains
with Very Small Holes
李明恭,黃宏財,李子才,游坤明
Leisure and Recreation Management
Tourism
mglee@chu.edu.tw
Abstract
For solving Laplace's equation in circular domains with circular holes, the null
field method (NFM) was developed by Chen and his research group (see
\cite{CS2009}). In \cite{LLHL2010} the explicit algebraic equations of the NFM
were provided, where some stability analysis was made. For the NFM, the
conservative schemes were proposed in \cite{LLHC2013}, and the algorithm
singularity was fully investigated in \cite{LLZHC2013}. To target on the same
problems, a new interior field method (IFM) was developed in \cite{HLLC2013}.
In addition to the NFM and the IFM, the collocation Trefftz method (CTM) is also
an effective boundary method. %This paper is devoted to a further study on NFM
and IFM. The goal of this paper is to apply those methods to Laplace's equation in
the circular domains with extremely small holes, which is also named as actually
punctured disks in this paper. By NFM, IFM, and CTM, numerical experiments are
carried out, and comparisons are provided.
Keyword：Null field method, collocation Trefftz method, small holes, Interior field
method