GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A fast level set method for propagating interfaces
Journal of Computational Physics
The immersed interface method: a numerical approach for partial differential equations with interfaces
A hybrid method for moving interface problems with application to the Hele-Shaw flow
Journal of Computational Physics
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
Journal of Computational Physics
The fast construction of extension velocities in level set methods
Journal of Computational Physics
A Supernodal Approach to Sparse Partial Pivoting
SIAM Journal on Matrix Analysis and Applications
Journal of Computational Physics
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
Journal of Computational Physics
A multigrid tutorial: second edition
A multigrid tutorial: second edition
A Cartesian grid embedded boundary method for the heat equation on irregular domains
Journal of Computational Physics
Maximum Principle Preserving Schemes for Interface Problems with Discontinuous Coefficients
SIAM Journal on Scientific Computing
The Immersed Interface/Multigrid Methods for Interface Problems
SIAM Journal on Scientific Computing
Reactive autophobic spreading of drops
Journal of Computational Physics
Transport and diffusion of material quantities on propagating interfaces via level set methods
Journal of Computational Physics
An Eulerian Formulation for Solving Partial Differential Equations Along a Moving Interface
Journal of Scientific Computing
A partial differential equation approach to multidimensional extrapolation
Journal of Computational Physics
Damascene Copper electroplating for chip interconnections
IBM Journal of Research and Development - Electrochemical microfabrication
Finite Differences And Partial Differential Equations
Finite Differences And Partial Differential Equations
Superconformal film growth: mechanism and quantification
IBM Journal of Research and Development - Electrochemical technology in microelectronics
The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains (Frontiers in Applied Mathematics)
An immersed interface method for Stokes flows with fixed/moving interfaces and rigid boundaries
Journal of Computational Physics
An algorithm for simulation of electrochemical systems with surface-bulk coupling strategies
Journal of Computational Physics
Hi-index | 31.46 |
We present a numerical algorithm for solving partial differential equations on irregular domains with moving interfaces. Instead of the typical approach of solving in a larger rectangular domain, our approach performs most calculations only in the desired domain. To do so efficiently, we have developed a one-sided multigrid method to solve the corresponding large sparse linear systems. Our focus is on the simulation of the electrodeposition process in semiconductor manufacturing in both two and three dimensions. Our goal is to track the position of the interface between the metal and the electrolyte as the features are filled and to determine which initial configurations and physical parameters lead to superfilling. We begin by motivating the set of equations which model the electrodeposition process. Building on existing models for superconformal electrodeposition, we develop a model which naturally arises from a conservation law form of surface additive evolution. We then introduce several numerical algorithms, including a conservative material transport level set method and our multigrid method for one-sided diffusion equations. We then analyze the accuracy of our numerical methods. Finally, we compare our result with experiment over a wide range of physical parameters.