A multigrid method for three-dimensional elasticity and algebraic convergence estimates
Applied Mathematics and Computation
A multi-grid algorithm for mixed problems with penalty
Numerische Mathematik
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
A nonconforming mixed multigrid method for the pure displacement problem in planar linear elasticity
SIAM Journal on Numerical Analysis
A Cartesian Grid Projection Method for the Incompressible Euler Equations in Complex Geometries
SIAM Journal on Scientific Computing
First-Order System Least Squares (FOSLS) for Planar Linear Elasticity: Pure Traction Problem
SIAM Journal on Numerical Analysis
A New Mixed Finite Element Formulation and the MAC Method for the Stokes Equations
SIAM Journal on Numerical Analysis
Block-Triangular Preconditioners for Saddle Point Problems with a Penalty Term
SIAM Journal on Scientific Computing
An Optimal Preconditioner for a Class of Saddle Point Problems with a Penalty Term
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Structural boundary design via level set and immersed interface methods
Journal of Computational Physics
Journal of Computational Physics
A Preconditioner for Substructuring Based on Constrained Energy Minimization
SIAM Journal on Scientific Computing
A fast solver for the Stokes equations with distributed forces in complex geometries
Journal of Computational Physics
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
First-order system least squares (FOSLS) for coupled fluid-elastic problems
Journal of Computational Physics
Journal of Computational Physics
A fast variational framework for accurate solid-fluid coupling
ACM SIGGRAPH 2007 papers
Journal of Computational Physics
Fictitious Domain Approach Via Lagrange Multipliers with Least Squares Spectral Element Method
Journal of Scientific Computing
Fictitious Domain approach with hp-finite element approximation for incompressible fluid flow
Journal of Computational Physics
Mimetic finite difference method for the Stokes problem on polygonal meshes
Journal of Computational Physics
Robust multigrid method for the planar linear elasticity problems
Numerische Mathematik
An efficient fluid-solid coupling algorithm for single-phase flows
Journal of Computational Physics
Tether Force Constraints in Stokes Flow by the Immersed Boundary Method on a Periodic Domain
SIAM Journal on Scientific Computing
An efficient multigrid method for the simulation of high-resolution elastic solids
ACM Transactions on Graphics (TOG)
An Eulerian method for multi-component problems in non-linear elasticity with sliding interfaces
Journal of Computational Physics
A second order virtual node method for elliptic problems with interfaces and irregular domains
Journal of Computational Physics
An Eulerian hybrid WENO centered-difference solver for elastic-plastic solids
Journal of Computational Physics
SIAM Journal on Scientific Computing
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We present a cut cell method in R^2 for enforcing Dirichlet and Neumann boundary conditions with nearly incompressible linear elastic materials in irregular domains. Virtual nodes on cut uniform grid cells are used to provide geometric flexibility in the domain boundary shape without sacrificing accuracy. We use a mixed formulation utilizing a MAC-type staggered grid with piecewise bilinear displacements centered at cell faces and piecewise constant pressures at cell centers. These discretization choices provide the necessary stability in the incompressible limit and the necessary accuracy in cut cells. Numerical experiments suggest second order accuracy in L^~. We target high-resolution problems and present a class of geometric multigrid methods for solving the discrete equations for displacements and pressures that achieves nearly optimal convergence rates independent of grid resolution.