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We develop a fast method to localize the level set method of Osher and Sethian (1988, J. Comput. Phys. 79, 12) and address two important issues that are intrinsic to the level set method: (a) how to extend a quantity that is given only on the interface to a neighborhood of the interface; (b) how to reset the level set function to be a signed distance(More)
In this paper, we present a weighted ENO (essentially non-oscillatory) scheme to approximate the viscosity solution of the Hamilton-Jacobi equation: = 0: This weighted ENO scheme is constructed upon and has the same stencil nodes as the 3 rd order ENO scheme but can be as high as 5 th order accurate in the smooth part of the solution. In addition to the(More)
Methods for generating adaptive grids are developed in this paper. Included is the static deformation method which generates a nal grid by 1 deforming an initial grid using artiicial time. Supersonic ows through two wedges are calculated by using the deformation method. A time accurate deformation method is also developed as a signiicant advancement of this(More)
In this paper we begin to explore the mathematical connection between equilibrium shapes of crystalline materials (Wull shapes) and shock wave structures in compressible gas dynamics (Riemann problems). These are radically diierent physical phenomena, but the similar nature of their discontinuous solutions suggests a connection. We show there is a precise(More)
We reproduce the general behavior of complicated bubble and droplet motions using the variational level set formulation introduced by the authors earlier. Our approach here ignores inertial effects; thus the motion is only correct as an approximation for very viscous problems. However, the steady states are true equilibrium solutions. Inertial forces will(More)
We develop a fast method to localize the level set method of Osher and Sethian (1988, J. Comput. Phys. 79, 12) and address two important issues that are intrinsic to the level set method: (a) how to extend a quantity that is given only on the interface to a neighborhood of the interface; (b) how to reset the level set function to be a signed distance(More)
As photomask critical dimensions shrink significantly below the exposure wavelength and the angle of off-axis illumination increases, the use of Kirchhoff thin mask approximation cannot capture diffraction and polarization effects that occur at a topographical mask surface. Such approximation errors result in inaccurate models that lead to poor prediction(More)
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