The geometric construction of finite element spaces suitable for complicated shapes or microstructured materials is discussed. As an application, the efficient computation of linearized elasticity is considered on them. Geometries are supposed to be implicitly described via 3D voxel data (e. g. μCT scans) associated with a cubic grid. We place degrees of freedom only at the grid nodes and incor...

7 Experiments with idealized geometry are used to compare model solutions of implicit VPand explicit EVP-solvers in two very different ice-ocean codes: the regular-grid, finite-volume Massachusetts Institute of Technology general circulation model (MITgcm) and the Alfred Wegener Institute Finite Element Ocean Model (FEOM). It is demonstrated that for both codes the obtained solutions of implici...

The author hereby grants to MIT permission to reproduce and to distribute publicly paper and electronic IBRARIES copies of this thesis document in whole or in part in any medium now known or hereafter created. Abstract This thesis project proposes a rapid visualization machine that can produce agile prototypes of simple architectural plans on a finite grid system. While various visualization sy...

Consider a small number of scouts exploring the infinite d-dimensional grid with the aim of hitting a hidden target point. Each scout is controlled by a probabilistic finite automaton that determines its movement (to a neighboring grid point) based on its current state. The scouts, that operate under a fully synchronous schedule, communicate with each other (in a way that affects their respecti...

The paper presents a convergence analysis of a multigrid solver for a system of linear algebraic equations resulting from the disretization of a convection-diffusion problem using a finite element method. We consider piecewise linear finite elements in combination with a streamline diffusion stabilization . We analyze a multigrid method that is based on canonical inter-grid transfer operators, ...

The scattering analysis from metallic Grid FSS consisting of rectangular perforations on a thick metallic screen illuminated by an oblique incident plane wave is presented. The grid structure is analyzed using Scale Changing Technique (SCT) which is based on the partition of the grid-plane into planar sub-domains defined at various scale-levels. Electromagnetic interaction between subsequent sc...

In this paper, we apply the high order WENO schemes to uniform cylindrical and spherical grid. Many 2-D and 3-D problems can be solved in 1-D equations if they have angular and radial symmetry. The reduced equations will typically involve geometric source terms. Therefore, conventional numerical schemes for Cartesian grid may not work well. We propose several approaches to apply the high order ...

Two-level finite element methods are applied to solve numerically the 2D/3D steady Navier-Stokes equations if a strong uniqueness condition ( ‖f‖ −1 ‖f‖0 ) 1 2 ≤ δ = 1 − N‖f‖ −1 ν2 holds, where N is defined in (2.4)-(2.6). Moreover, one-level finite element method is applied to solve numerically the 2D/3D steady Navier-Stokes equations if a weak uniqueness condition 0 < δ < ( ‖f‖ −1 ‖f‖0 ) 1 2 ...

We propose an a-posteriori error/smoothness indicator for standard semidiscrete finite volume schemes for systems of conservation laws, based on the numerical production of entropy. This idea extends previous work by the first author limited to central finite volume schemes on staggered grids. We prove that the indicator converges to zero with the same rate of the error of the underlying numeri...

Consider a small group of mobile agents whose goal is to locate a certain cell in a two-dimensional infinite grid. The agents operate in an asynchronous environment, where in each discrete time step, an arbitrary subset of the agents execute one atomic look-compute-move cycle. The protocol controlling each agent is determined by a (possibly distinct) finite automaton. The only means of communic...