Linda Stals

Two-dimensional simulation of plasma-based ion implantation

A particle-in-cell simulation is used to study the time-dependent evolution of the potential and the electrical field surrounding two-dimensional objects during a high voltage pulse in the context of plasma immersion ion implantation. The numerical procedure is based on the solution of Poisson’s equation on a grid and the determination of the movement of the particles through the grid. Ion current density, implanted concentration, average impact energy, and impact angle of the ions were calculated using this method for two geometrical shapes, a square and an L-shaped object. The nonuniformity of the sheath potential near convex and concave corners is shown. The divergence of the electrical field in the vicinity of corners leads to dramatically reduced concentration of the incident ions. The simulation also shows that a large ion flux hits the surface during the rise time of the pulse. Directly after the rise time, more than 40% of the whole concentration is implanted. Hence, the average impact energy of t...

Simulation of trench homogeneity in plasma immersion ion implantation

The time-dependent evolution of the potential, the electrical field, and the particle movement surrounding two-dimensional trenches during a high voltage pulse in the context of plasma immersion ion implantation is studied by a particle-in-cell simulation. The numerical procedure is based on the solution of Poisson‘s equation on a grid and the determination of the movement of the particles on the grid. This simulation is combined with simulation codes for the calculation of depth profiles and sputtering yields. The retained ion dose and the depth resolved concentration distribution were determined in dependence on the rise time of the pulse between 0.1 and 2 μs, pulse durations between 1 and 10 μs and the ion mass (m=20–131, i.e., Ne,…,Xe) for trenches with two different aspect ratios (η=3:1 and 3:2). The results are discussed on the basis of the temporal evolution of the energy of the ions and the impact angle of the ions during the pulse.

Fault-Tolerant Grid-Based Solvers: Combining Concepts from Sparse Grids and MapReduce

Abstract A key issue confronting petascale and exascale computing is the growth in probability of soft and hard faults with increasing system size. A promising approach to this problem is the use of algorithms that are inherently fault tolerant. We introduce such an algorithm for the solution of partial differential equations, based on the sparse grid approach. Here, the solution of multiple component grids are efficiently combined to achieve a solution on a full grid. The technique also lends itself to a (modified) MapReduce framework on a cluster of processors, with the map stage corresponding to allocating each component grid for solution over a subset of the processors, and the reduce stage corresponding to their combination. We describe how the sparse grid combination method can be modified to robustly solve partial differential equations in the presence of faults. This is based on a modified combination formula that can accommodate the loss of one or two component grids. We also discuss accuracy issues associated with this formula. We give details of a prototype implementation within a MapReduce framework using the dynamic process features and asynchronous message passing facilities of MPI. Results on a two-dimensional advection problem show that the errors after the loss of one or two sub-grids are within a factor of 3 of the sparse grid solution in the presence of no faults. They also indicate that the sparse grid technique with four times the resolution has approximately the same error as a full grid, while requiring (for a sufficiently high resolution) much lower computation and memory requirements. We finally outline a MapReduce variant capable of responding to faults in ways other than re-scheduling of failed tasks. We discuss the likely software requirements for such a flexible MapReduce framework, the requirements it will impose on users’ legacy codes, and the systems runtime behavior.

Nonstationary iterated Tikhonov regularization for ill-posed problems in Banach spaces

Nonstationary iterated Tikhonov regularization is an efficient method for solving ill-posed problems in Hilbert spaces. However, this method may not produce good results in some situations since it tends to oversmooth solutions and hence destroy special features such as sparsity and discontinuity. By making use of duality mappings and Bregman distance, we propose an extension of this method to the Banach space setting and establish its convergence. We also present numerical simulations which indicate that the method in Banach space setting can produce better results.

Managing complexity in the Parallel Sparse Grid Combination Technique

J. W. Larson, P. E. Strazdins, M. Hegland, B. Harding, S. Roberts , L. Stals , A. P. Rendell, Md. M. Ali , and J. Southern

Adaptive multigrid in parallel

Early experiments with parallel multigrid used square domains and uniform grids. More recently, several authors have considered problems with more complicated domains (see for example McCormicks AFAC method (1989) and Baden et al. (1994)). However, these methods still use structured grids. In this paper we present a program which is based upon unstructured grids. By allowing unstructured grids we can solve problems on more general regions and use adaptive refinement methods.<<ETX>>

A note on three stochastic processes with immigration

Three stochastic processes, the birth, death and birth-death processes, subject to immigration can be decomposed into the sum of each process in the absence of immigration and an independent process. We examine these independent processes through their probability generating functions (pgfs) and derive their expectations.

Teaching Computational Science Using VPython and Virtual Reality

The Australian National University has two new complemen- tary computational science programs, the Bachelor of Computational Science and the eScience graduate program. Students from the eScience program have developed sophisticated visualisation projects which have then been used to educate current and prospective undergraduate stu- dents in the Bachelor program. In this paper we will discuss the use of VPython combined with a 3D visualisation theatre, the Wedge, to pro- duce hands-on computational science tutorials which we use to motivate computational science. We will briefly describe the use of VPython in our outreach tutorials, in particular a bouncing ball and gas simulation tutorial. The wedge virtual reality environment is also described as is the porting of VPython to the Wedge. Overall we provide a glimpse into our coordinated approach to using high level visualisation and virtual reality in the promotion of computational science.

Simulation of plasma-immersed implantation of trenches

The results of a particle-in-cell simulation for the plasma system in the plasma immersion ion implantation context is presented. PIII of two-dimensional trenches is studied using this simulation. Modeling of the potential around the trenches and the development of the plasma sheath in dependence on the pulse time is demonstrated. The implanted concentration, the average impact ion angle and the ion energy are computed as function of the pulse time and discussed in dependence on the aspect ratios of trenches.

A Mixed Finite Element Discretisation of Thin Plate Splines Based on Biorthogonal Systems

The thin plate spline method is a widely used data fitting technique as it has the ability to smooth noisy data. Here we consider a mixed finite element discretisation of the thin plate spline. By using mixed finite elements the formulation can be defined in-terms of relatively simple stencils, thus resulting in a system that is sparse and whose size only depends linearly on the number of finite element nodes. The mixed formulation is obtained by introducing the gradient of the corresponding function as an additional unknown. The novel approach taken in this paper is to work with a pair of bases for the gradient and the Lagrange multiplier forming a biorthogonal system thus ensuring that the scheme is numerically efficient, and the formulation is stable. Some numerical results are presented to demonstrate the performance of our approach. A preconditioned conjugate gradient method is an efficient solver for the arising linear system of equations.