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- Catherine Kublik, Nicolay M. Tanushev, Yen-Hsi Richard Tsai
- J. Comput. Physics
- 2013

We propose a simple formulation for constructing boundary integral methods to solve Poisson’s equation on domains with piecewise smooth boundaries defined through their signed distance function. Our formulation is based on averaging a family of parameterizations of an integral equation defined on the boundary of the domain, where the integrations are… (More)

- Catherine Kublik, Selim Esedoglu, Jeffrey A. Fessler
- SIAM J. Scientific Computing
- 2011

We propose efficient and accurate algorithms for computing certain area preserving geometric motions of curves in the plane, such as area preserving motion by curvature. These schemes are based on a new class of diffusion generated motion algorithms using signed distance functions. In particular, they alternate two very simple and fast operations, namely… (More)

We propose a new formulation using the closest point mapping for integrating over smooth curves and surfaces with boundaries that are described by their closest point mappings. Contrary to the common practice with level set methods, the volume integrals derived from our formulation coincide exactly with the surface or line integrals that one wish to… (More)

We use Lyapunov functionals to obtain sufficient conditions that guarantee exponential stability of the zero solution of the finite delay Volterra difference equation x(t + 1) = a(t)x(t) + t−1 ∑ s=t−r b(t, s)x(s). Also, by displaying a slightly different Lyapunov functional we obtain conditions that guarantee the instability of the zero solution. The… (More)

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