Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Applications of spatial data structures: Computer graphics, image processing, and GIS
Applications of spatial data structures: Computer graphics, image processing, and GIS
The design and analysis of spatial data structures
The design and analysis of spatial data structures
SIAM Journal on Numerical Analysis
A numerical method for solving incompressible viscous flow problems
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Journal of Computational Physics
Tree methods for moving interfaces
Journal of Computational Physics
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
Journal of Computational Physics
A boundary condition capturing method for Poisson's equation on irregular domains
Journal of Computational Physics
Structural boundary design via level set and immersed interface methods
Journal of Computational Physics
Journal of Computational Physics
Physically based modeling and animation of fire
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
A second-order-accurate symmetric discretization of the Poisson equation on irregular domains
Journal of Computational Physics
A Level Set Approach for the Numerical Simulation of Dendritic Growth
Journal of Scientific Computing
A partial differential equation approach to multidimensional extrapolation
Journal of Computational Physics
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
Local level set method in high dimension and codimension
Journal of Computational Physics
Journal of Computational Physics
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
An efficient fluid-solid coupling algorithm for single-phase flows
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.45 |
We present a numerical method for solving the equations of linear elasticity on irregular domains in two and three spatial dimensions. We combine a finite volume and a finite difference approaches to derive discretizations that produce second-order accurate solutions in the L^~-norm. Our discretization is 'sharp' in the sense that the physical boundary conditions (mixed Dirichlet/Neumann-type) are imposed at the interface and the solution is computed inside the irregular domain only, without the need of smearing the solution across the interface. The irregular domain is represented implicitly using a level-set function so that this approach is applicable to free moving boundary problems; we provide a simple example of shape optimization to illustrate this capability. In addition, we provide an extension of our method to the case of adaptive meshes in both two and three spatial dimensions: we use non-graded quadtree (2D) and octree (3D) data structures to represent the grid that is automatically refined near the irregular domain's boundary. This extension to quadtree/octree grids produces second-order accurate solutions albeit non-symmetric linear systems, due to the node-based sampling nature of the approach. However, the linear system can be solved with simple linear solvers; in this work we use the BICGSTAB algorithm.