
Biography
Georgios Diamantopoulos was born in Athens,Greece in 1988. He holds a degree in applied mathematics from the University of Crete, Greece and a Master's degree in computational engineering from the FriedrichAlexander University of ErlangenNuremberg, Germany. He joined the Institute for Microelectronics on January 2016 as a research assistant. He is researching high performance numerical approaches for Technology CAD within the scope of the Christian Doppler Laboratory for High Performance TCAD.
Parallel Fast Marching Method for Redistancing Problems
A common task in process TCAD is the simulation of an interface evolution over time. One of the steps in the simulation is the recalculation of the distance from the interface. After performing one (or more) advection step(s) on the interface, the distance from the interface is distorted. A recalculation of the distance is therefore necessary in order to maintain the signeddistance property of the field.
This redistancing process (i.e. recalculation of the distance) can be treated as an expanding front problem with a unit speed, and it can be described by the Eikonal equation. This problem not only occurs in microelectronics but also in other fields, such as computer vision, computational fluid dynamics, computational geometry, material science, etc.
A widely used method for the solution of the Eikonal equation is the fast marching method (FMM). It is a noniterative, highly accurate method. However, the sequential nature of the algorithm is not conducive to a straightforward parallelization. Many parallelization approaches have been put forth 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 have been limited to synthetic pointbased problem cases that do not cover the much more challenging cases of interface redistancing, in which, instead of simplistic point sets, challenging interface geometries are processed.
We filled this gap by evaluating a sharedmemory implementation of the parallel FMM for interfaces inspired by practical problems and for different domain decomposition scenarios. One of these interfaces is the step problem displayed in Fig. 1. The parallel efficiency and runtime performance was examined on a dualsocket Ivy BridgeEP compute node. As can be observed in Fig. 2, this method shows good scalability for the case where the interface is (close to) evenly partitioned among the subdomains. On the other hand, poor performance has been observed in the case of uneven domain decomposition. Our analyses outline the feasibility limits of a sharedmemory parallel FMM.
Fig. 1: Planar surface in XY with a step in the domain [0.96,0.96]^{3}. The interface is in grey. The numerical solution is displayed: High values are represented with red hues and low values with blue hues.
Fig. 2: Parallel speedup for the step case with various partitions. The speedup is good for the decomposition in the ydirection but poor for the xydirection and even poorer for the xdirection. Decomposing the domain in the ydirection results in a loadbalanced domain decomposition. On the other hand, a domain decomposition in the xdirection results in an inhomogeneous decomposition, which necessitates additional calculations in order to reach the solution for the parallel algorithm.