We summarize the properties of eigenvalues and eigenfunctions of the Laplace operator in
bounded Euclidean domains with Dirichlet, Neumann, or Robin boundary condition. We …

We derive a general exact formula for the mean first passage time (MFPT) from a fixed point
inside a planar domain to an escape region on its boundary. The underlying mixed Dirichlet …

This is a unique monograph on numerical conformal mapping that gives a comprehensive
account of the theoretical, computational and application aspects of the problems of …

In the early 1980s an elementary algorithm for computing conformal maps was discovered
by R. Kühnau and the first author. The algorithm is fast and accurate, but convergence was …

This paper proposes a unified semi-analytical method for the free in-plane and out-of-plane
vibrations of arbitrarily shaped plates with clamped edges. The method is derived using …

We report recent progress in the computation of conformal mappings from surfaces with
arbitrary topologies to canonical domains. Two major computational methodologies are …

This paper presents a fast boundary integral equation method for approximating the
conformal mapping from bounded and unbounded multiply connected regions of …

Conformal Mapping in Linear Time Page 1 Discrete Comput Geom (2010) 44: 330–428 DOI
10.1007/s00454-010-9269-9 Conformal Mapping in Linear Time Christopher J. Bishop …

Isogeometric analysis has brought a paradigm shift in integrating computational simulations
with geometric designs across engineering disciplines. This technique necessitates analysis …

Computational conformal geometry is an inter-disciplinary field between mathematics and
computer science. This work introduces the fundamentals of computational conformal …