131,131 research outputs found
A Second-Order Formulation of Non-Termination
We consider the termination/non-termination property of a class of loops.
Such loops are commonly used abstractions of real program pieces. Second-order
logic is a convenient language to express non-termination. Of course, such
property is generally undecidable. However, by restricting the language to
known decidable cases, we exhibit new classes of loops, the non-termination of
which is decidable. We present a bunch of examples.Comment: 8 page
Application of edge-based finite elements and vector ABCs in 3D scattering
A finite element absorbing boundary condition (FE-ABC) solution of the scattering by arbitrary 3-D structures is considered. The computational domain is discretized using edge-based tetrahedral elements. In contrast to the node-based elements, edge elements can treat geometries with sharp edges, are divergence-less, and easily satisfy the field continuity condition across dielectric interfaces. They do, however, lead to a higher unknown count but this is balanced by the greater sparsity of the resulting finite element matrix. Thus, the computation time required to solve such a system iteratively with a given degree of accuracy is less than the traditional node-based approach. The purpose is to examine the derivation and performance of the ABC's when applied to 2-D and 3-D problems and to discuss the specifics of our FE-ABC implementation
Numerical Methods for a Nonlinear BVP Arising in Physical Oceanography
In this paper we report and compare the numerical results for an ocean
circulation model obtained by the classical truncated boundary formulation, the
free boundary approach and a quasi-uniform grid treatment of the problem. We
apply a shooting method to the truncated boundary formulation and finite
difference methods to both the free boundary approach and the quasi-uniform
grid treatment. Using the shooting method, supplemented by the Newton's
iterations, we show that the ocean circulation model cannot be considered as a
simple test case. In fact, for this method we are forced to use as initial
iterate a value close to the correct missing initial condition in order to be
able to get a convergent numerical solution. The reported numerical results
allow us to point out how the finite difference method with a quasi-uniform
grid is the less demanding approach and that the free boundary approach
provides a more reliable formulation than the classical truncated boundary
formulation.Comment: 25 pages, 12 figures, 5 table
- …