A continuum method for modeling surface tension
Journal of Computational Physics
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
SIAM Review
Journal of Computational Physics
A front-tracking method for the computations of multiphase flow
Journal of Computational Physics
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
Semi-Implicit Level Set Methods for Curvature and Surface Diffusion Motion
Journal of Scientific Computing
Simplicial isosurfacing in arbitrary dimension and codimension
Journal of Computational Physics
A partial differential equation approach to multidimensional extrapolation
Journal of Computational Physics
Local level set method in high dimension and codimension
Journal of Computational Physics
Numerical approximations of singular source terms in differential equations
Journal of Computational Physics
Discretization of Dirac delta functions in level set methods
Journal of Computational Physics
The numerical approximation of a delta function with application to level set methods
Journal of Computational Physics
Two methods for discretizing a delta function supported on a level set
Journal of Computational Physics
A second order accurate level set method on non-graded adaptive cartesian grids
Journal of Computational Physics
Geometric integration over irregular domains with application to level-set methods
Journal of Computational Physics
A convergence rate theorem for finite difference approximations to delta functions
Journal of Computational Physics
Finite difference methods for approximating Heaviside functions
Journal of Computational Physics
High order numerical methods to two dimensional delta function integrals in level set methods
Journal of Computational Physics
Journal of Computational Physics
High Order Numerical Methods to Three Dimensional Delta Function Integrals in Level Set Methods
SIAM Journal on Scientific Computing
Journal of Computational Physics
Optimal reconstruction of material properties in complex multiphysics phenomena
Journal of Computational Physics
Hi-index | 31.48 |
We present a robust second-order accurate method for discretizing the multi-dimensional Heaviside and the Dirac delta functions on irregular domains. The method is robust in the following ways: (1) integrations of source terms on a co-dimension one surface are independent of the underlying grid and therefore stable under perturbations of the domain's boundary; (2) the method depends only on the function value of a level function, not on its derivatives. We present the discretizations in tabulated form to make their implementations straightforward. We present numerical results in two and three spatial dimensions to demonstrate the second-order accuracy in the L^1-norm in the case of the solution of PDEs with singular source terms. In the case of evaluating the contribution of singular source terms on interfaces, the method is also second-order accurate in the L^~-norm.