A monotone convergence theorem for Newton-like methods using hypotheses on divided differences of order two.
A Monte Carlo Method for High Dimensional Integration.
A Moreau-Yosida regularization of a difference of two convex functions.
A mountain pass method for the numerical solution of semilinear wave equations.
A moving mesh fictitious domain approach for shape optimization problems
A moving mesh fictitious domain approach for shape optimization problems
A new numerical method based on fictitious domain methods for shape optimization problems governed by the Poisson equation is proposed. The basic idea is to combine the boundary variation technique, in which the mesh is moving during the optimization, and efficient fictitious domain preconditioning in the solution of the (adjoint) state equations. Neumann boundary value problems are solved using an algebraic fictitious domain method. A mixed formulation based on boundary Lagrange multipliers is...
A multi-dimensional Hausdorff moment problems regularization by finite moments.
A multidomain spectral collocation method for the Stokes problem.
A multigrid algorithm for higher order finite elements on sparse grids.
A Multi-Grid Algorithm for Mixed Problems with Penalty.
A multigrid algorithm for solving the multi-group, anisotropic scattering Boltzmann equation using first-order system least-squares methodology.
A Multigrid Method for a Parameter Dependent Problem in Solid Mechanics.
A multigrid method for a Petrov-Galerkin discretization of the Stokes equations.
A multigrid method for distributed parameter estimation problems.
A multigrid method for Reissner-Mindlin plates.
A multigrid method for saddle point problems arising from mortar finite element discretizations.
A multilevel adaptive mesh generation scheme using Kd-trees.
A Multilevel Algorithm for the Biharmonic Problem.
A multilevel method with correction by aggregation for solving discrete elliptic problems
The author studies the behaviour of a multi-level method that combines the Jacobi iterations and the correction by aggragation of unknowns. Our considerations are restricted to a simple one-dimensional example, which allows us to employ the technique of the Fourier analysis. Despite of this restriction we are able to demonstrate differences between the behaviour of the algorithm considered and of multigrid methods employing interpolation instead of aggregation.
A multilevel Newton's method for eigenvalue problems
We propose a new type of multilevel method for solving eigenvalue problems based on Newton's method. With the proposed iteration method, solving an eigenvalue problem on the finest finite element space is replaced by solving a small scale eigenvalue problem in a coarse space and a sequence of augmented linear problems, derived by Newton step in the corresponding sequence of finite element spaces. This iteration scheme improves overall efficiency of the finite element method for solving eigenvalue...