The Fast Marching Method is widely used for the solution of the Eikonal equation in problems arising in science and engineering applications. A common application is the calculation of the distance to an interface resulting in a signed distance field. The Fast Marching Method is a non-iterative high accuracy method. However, the sequential nature of the algorithm does not favor a straightforward parallelization. Many parallelization approaches have been presented so far, but they do not provide a reasonable parallel efficiency. Recently, a promising new approach based on an overlapping domain decomposition technique has been introduced, providing a scalable, widely applicable parallel algorithm. However, investigations so far were limited to synthetic point-based problem cases which do not cover the much more challenging cases of interface re-distancing, where instead of simplistic point sets, challenging interface geometries are processed. In this work we fill this gap by analyzing a shared-memory implementation of the parallel Fast Marching Method for three-dimensional interface problems, covering the key challenges and various domain decomposition strategies. The parallel efficiency and run-time performance is examined on a dual-socket Ivy Bridge-EP compute node. Our analyses clearly outline the feasibility limits of a shared-memory parallel Fast Marching Method.

This paper presents an anisotropic adaptation strategy for three-dimensional unstructured tetrahedral meshes, which allows us to produce thin mostly anisotropic layers at the outside margin, i.e., the skin of an arbitrary meshed simulation domain. An essential task for any modern algorithm in the finite-element solution of partial differential equations, especially in the field of semiconductor process and device simulation, the major application is to provide appropriate resolution of the partial discretization mesh. The start-up conditions for semiconductor process and device simulations claim an initial mesh preparation that is performed by so-called Laplace refinement. The basic idea is to solve Laplace's equation on an initial coarse mesh with Dirichlet boundary conditions. Afterward, the gradient field is used to form an anisotropic metric that allows to refine the initial mesh based on tetrahedral bisection

We deal with problems arising in the coupling of process and device simulators. It is analyzed what kind of data and algorithms such simulations are based on. An overview of existing technology computer-aided design data models is given. A generic object-oriented data model suitable for three-dimensional process and device simulations, the so-called WAFER-STATE-SERVER is presented. By taking advantage of object-oriented abstraction mechanisms, key tasks in the coupling of simulators are relocated from the simulator into the WAFER-STATE-SERVER. The new data model allows an efficient data exchange between existing process and device simulators. It is capable of managing geometries of different dimensions, and handling grids and distributed quantities stored therein. The data model also defines algorithms to perform geometrical operations as they occur in topography simulations. Three process simulators based on the new data model were developed, one of which is presented in this work.

An algorithm for smoothing results of three-dimensional (3-D) Monte Carlo ion implantation simulations and translating them from the grid used for the Monte Carlo simulation to an arbitrary unstructured 3-D grid is presented. This algorithm is important for joining various process simulation steps, where data have to be smoothed or transferred from one grid to another. Furthermore, it is important for integrating the ion implantation simulator into a process flow. One reason for using different grids is that for certain Monte Carlo simulation methods, using orthogrids is mandatory because of performance reasons. The algorithm presented sweeps a small rectangular grid over the points of the new tetrahedral grid and uses approximation by generalized Bernstein polynomials. This approach was put on a mathematically sound basis by proving several properties of these polynomials. It does not suffer from the adverse effects of least squares fits of polynomials of fixed degree as known from the response surface method. The most important properties of Bernstein polynomials generalized to cuboid domains are presented, including uniform convergence, an asymptotic formula, and the variation diminishing property. The smoothing algorithm which works very fast is described and, in order to show its applicability, the resulting values of a 3-D real world implantation example are given and compared with those of a least squares fit of a multivariate polynomial of degree two, which yielded unusable results.

We present a parallelization method based on message passing interface (MPI) for a Monte Carlo program for two-dimensional (2-D) and three-dimensional (3-D) simulation of ion implantations. We use a master-slave strategy where the master process synchronizes the slaves and performs the input-output operations, while the slaves perform the physical simulation. For this method the simulation domain is geometrically distributed among several CPU's which have to exchange only very little information during the simulation. Thereby, the communication overhead between the CPU's is kept so low that it has almost no influence on the performance gain even if a standard network of workstations is used instead of a massively parallel computer to perform the simulation. We have optimized the performance gain by identifying bottlenecks of this strategy when it is applied to arbitrary geometries consisting of various materials. This requires the application of different physical models within the simulation domain and makes it impossible to determine a reasonable domain distribution before starting the simulation. Due to a feedback between master and slaves by online performance measurements, we obtain an almost linear performance gain on a cluster of workstations with just slightly varying processor loads. Besides the increase in performance, the parallelization method also achieves a distribution of the required memory. This allows 3-D simulations on a cluster of workstations, where each single machines would not have enough memory to perform the simulation on its own.