Analysis of a one-dimensional model for the immersed boundary method
SIAM Journal on Numerical Analysis
A front-tracking method for dendritic solidification
Journal of Computational Physics
Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
SIAM Journal on Scientific Computing
A front-tracking method for the computations of multiphase flow
Journal of Computational Physics
Regularization Techniques for Numerical Approximation of PDEs with Singularities
Journal of Scientific Computing
Discretization of Dirac delta functions in level set methods
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
The numerical approximation of a delta function with application to level set methods
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Two methods for discretizing a delta function supported on a level set
Journal of Computational Physics
An improved direct-forcing immersed-boundary method for finite difference applications
Journal of Computational Physics
An adaptive, formally second order accurate version of the immersed boundary method
Journal of Computational Physics
Journal of Computational Physics
Level Set Calculations for Incompressible Two-Phase Flows on a Dynamically Adaptive Grid
Journal of Scientific Computing
On Boundary Condition Capturing for Multiphase Interfaces
Journal of Scientific Computing
Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A coupling interface method for elliptic interface problems
Journal of Computational Physics
High order numerical methods to a type of delta function integrals
Journal of Computational Physics
Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities
Journal of Computational Physics
A kernel-free boundary integral method for elliptic boundary value problems
Journal of Computational Physics
Short Note: A proof that a discrete delta function is second-order accurate
Journal of Computational Physics
On the numerical solution of diffusion-reaction equations with singular source terms
Journal of Computational and Applied Mathematics
A convergence rate theorem for finite difference approximations to delta functions
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Finite difference methods for approximating Heaviside functions
Journal of Computational Physics
Discretizing delta functions via finite differences and gradient normalization
Journal of Computational Physics
Journal of Scientific Computing
High order numerical methods to two dimensional delta function integrals in level set methods
Journal of Computational Physics
A sharp interface finite volume method for elliptic equations on Cartesian grids
Journal of Computational Physics
Journal of Computational Physics
On the accuracy of direct forcing immersed boundary methods with projection methods
Journal of Computational Physics
Journal of Computational Physics
Multiresolution simulations using particles
VECPAR'06 Proceedings of the 7th international conference on High performance computing for computational science
The Immersed Structural Potential Method for haemodynamic applications
Journal of Computational Physics
Augmented coupling interface method for solving eigenvalue problems with sign-changed coefficients
Journal of Computational Physics
Numerical Method for Interaction Among Multi-particle, Fluid and Arbitrary Shape Structure
Journal of Scientific Computing
High Order Numerical Methods to Three Dimensional Delta Function Integrals in Level Set Methods
SIAM Journal on Scientific Computing
MIB method for elliptic equations with multi-material interfaces
Journal of Computational Physics
Short note: A note on pressure accuracy in immersed boundary method for Stokes flow
Journal of Computational Physics
Spectral collocation and radial basis function methods for one-dimensional interface problems
Applied Numerical Mathematics
Journal of Computational Physics
A level-set continuum method for two-phase flows with insoluble surfactant
Journal of Computational Physics
Journal of Scientific Computing
An embedded boundary method for soluble surfactants with interface tracking for two-phase flows
Journal of Computational Physics
A numerical method for two-phase flows of dense granular mixtures
Journal of Computational Physics
Hi-index | 31.62 |
Singular terms in differential equations pose severe challenges for numerical approximations on regular grids. Regularization of the singularities is a very useful technique for their representation on the grid. We analyze such techniques for the practically preferred case of narrow support of the regularizations, extending our earlier results for wider support. The analysis also generalizes existing theory for one dimensional problems to multi-dimensions. New high order multi-dimensional techniques for differential equations and numerical quadrature are introduced based on the analysis and numerical results are presented. We also show that the common use of distance functions in level-set methods to extend one dimensional regularization to higher dimensions may produce O(1) errors.