Proof. Clearly, this problem is in NP, since one can easily guess the coverage path of the robot and then verify its probability of surviving it in polynomial time. To prove its NP-hardness, we use a reduction from the Hamiltonian path problem on grid graphs. A grid graph is a finite node-induced subgraph of the infinite two-dimensional integer grid (see Figure 1 for an example of a general gri...

Full wave equation 2D modeling and migration using a new finite difference scheme based on the Galerkin method (FDGM) for irregular grids are presented. Since these involve semi-discretization by the finite element method (FEM) in the depth direction with the linear element, spatially irregular grids can be used to compute the wavefield in modeling and reverse-time migration. The mesh can be ma...

The objective of this study is to conduct a unified computational analysis for computing design parameters such as axial thrust, convective and radiative wall heat fluxes for regeneratively cooled liquid rocket engine nozzles, so as to develop a computational strategy for computing those parameters through parametric investigations. The computational methodology is based on a multidimensional, ...

We consider the problem of translating a (finite or infinite) square grid G over a set S of n points in the plane in order to maximize some objective function. We say that a grid cell is k-occupied if it contains k or more points of S. The main set of problems we study have to do with translating an infinite grid so that the number of k-occupied cells is maximized or minimized. For these proble...

j An adaptive grid, finite-volume method has been used to solve the NavierStokes equations for complete (forebody and afterbody) flowfields around blunt belies. The code, which is applicable for axisymmetric cr two-dimensional flows, allows the mesh to adjust during the computation to provide a closer spacing of mesh points in regions of high gradients, thus minimizing the number of required co...

We present here the first results of a work on a multiscale resolution method using both Finite Volumes and Elements. Our method relies upon the coupling of grid scales: a coarse one and a fine one. The trick is to build a Finite Element basis on the coarse grid from problems solved on the fine one. In previous works on this subject [1] [2], the Finite Element method was used in both the fine a...

The use of a discretization grid in particle-in-cell methods is responsible for the nite-grid instability. The instability is a spurious numerical e ect due to the aliasing of di erent Fourier modes, that are undistinguished by the computational grid but have di erent e ects on the particles. The nite-grid instability has been studied thoroughly in uniform grids [1, 2]; a linear theory has been...

Consider a group of mobile finite automata, referred to as agents, located in the origin of an infinite grid. The grid is occupied by obstacles, i.e., sets of cells that can not be entered by the agents. In every step, an agent can sense the states of the co-located agents and is allowed to move to any neighboring cell of the grid not blocked by an obstacle. We assume that the circumference of ...