Josef Weinbub

Automatic performance optimization in ViennaCL for GPUs

Highly parallel computing architectures such as graphics processing units (GPUs) pose several new challenges for scientific computing, which have been absent on single core CPUs. However, a transition from existing serial code to parallel code for GPUs often requires a considerable amount of effort. The Vienna Computing Library (ViennaCL) presented in the beginning of this work is based on OpenCL to support a wide range of hardware and aims at providing a high-level C++ interface that is mostly compatible with the existing CPU linear algebra library uBLAS shipped with the Boost libraries. As a general purpose linear algebra library, ViennaCL runs on a variety of GPU boards from different vendors pursuing different hardware architectures. As a consequence, the optimal number of threads working on a problem in parallel depends on the available hardware and the algorithm executed thereon. We present an optimization framework, which extracts suitable thread numbers and allows ViennaCL to automatically optimize itself to the underlying hardware. The performance enhancement of individually tuned kernels over default parameter choices range up to 25 percent for the kernels considered on high-end hardware, and up to a factor of seven on low-end hardware.

Pipelined Iterative Solvers with Kernel Fusion for Graphics Processing Units

We revisit the implementation of iterative solvers on discrete graphics processing units and demonstrate the benefit of implementations using extensive kernel fusion for pipelined formulations over conventional implementations of classical formulations. The proposed implementations with both CUDA and OpenCL are freely available in ViennaCL and are shown to be competitive with or even superior to other solver packages for graphics processing units. The highest-performance gains are obtained for small to medium-sized systems, while our implementations are on par with vendor-tuned implementations for very large systems. Our results are especially beneficial for transient problems, where many small to medium-sized systems instead of a single big system need to be solved.

Growth rates of dry thermal oxidation of 4H-silicon carbide

We provide a full set of growth rate coefficients to enable high-accuracy two- and three-dimensional simulations of dry thermal oxidation of 4H-silicon carbide. The available models are insufficient for the simulation of complex multi-dimensional structures, as they are unable to predict oxidation for arbitrary crystal directions because of the insufficient growth rate coefficients. By investigating time-dependent dry thermal oxidation kinetics, we obtain temperature-dependent growth rate coefficients for surfaces with different crystal orientations. We fit experimental data using an empirical relation to obtain the oxidation growth rate parameters. Time-dependent oxide thicknesses at various temperatures are taken from published experimental findings. We discuss the oxidation rate parameters in terms of surface orientation and oxidation temperature. Additionally, we fit the obtained temperature-dependent growth rate coefficients using the Arrhenius equation to obtain activation energies and pre-exponenti...

The meshing framework ViennaMesh for finite element applications

The applicability of the meshing framework ViennaMesh for finite element simulations is investigated. Meshing tools are highly diverse, meaning that each software package offers specific properties, such as the conforming Delaunay property. The feasibility of these properties tends to be domain specific, thus restricting the general application of a meshing tool. For research purposes, it is desirable to have a rich toolset consisting of the various meshing packages in order to be able to quickly apply the various packages to the problem at hand. Different meshing tools have to be utilized to support a broader range of mesh properties. Further contributing to this problem is the lack of a common programming interface, impeding convenient switching of meshing backends. ViennaMesh tackles this challenge by providing a uniform meshing interface and reusable mesh-related tools, like CGAL, Gmsh, Netgen, and Tetgen. We depict the feasibility of our approach by discussing two applications relevant to finite element simulations, being a local mesh optimization and an adaptive mesh refinement application.

ViennaCL---Linear Algebra Library for Multi- and Many-Core Architectures

CUDA, OpenCL, and OpenMP are popular programming models for the multicore architectures of CPUs and many-core architectures of GPUs or Xeon Phis. At the same time, computational scientists face the question of which programming model to use to obtain their scientific results. We present the linear algebra library ViennaCL, which is built on top of all three programming models, thus enabling computational scientists to interface to a single library, yet obtain high performance for all three hardware types. Since the respective compute back end can be selected at runtime, one can seamlessly switch between different hardware types without the need for error-prone and time-consuming recompilation steps. We present new benchmark results for sparse linear algebra operations in ViennaCL, complementing results for the dense linear algebra operations in ViennaCL reported in earlier work. Comparisons with vendor libraries show that ViennaCL provides better overall performance for sparse matrix-vector and sparse mat...

Performance portability study of linear algebra kernels in OpenCL

The performance portability of OpenCL kernel implementations for common memory bandwidth limited linear algebra operations across different hardware generations of the same vendor as well as across vendors is studied. Certain combinations of kernel implementations and work sizes are found to exhibit good performance across compute kernels, hardware generations, and, to a lesser degree, vendors. As a consequence, it is demonstrated that the optimization of a single kernel is often sufficient to obtain good performance for a large class of more complicated operations.

Using Temporary Explicit Meshes for Direct Flux Calculation on Implicit Surfaces

Abstract We focus on a surface evolution problem where the surface is represented as a narrow-band level-set and the local surface speed is defined by a relation to the direct visibility of a source plane above the surface. A level-set representation of the surface can handle complex evolutions robustly and is therefore a frequently encountered choice. Ray tracing is used to compute the visibility of the source plane for each surface point. Commonly, rays are traced directly through the level-set and the already available (hierarchical) volume data structure is used to efficiently perform intersection tests. We present an approach that performs ray tracing on a temporarily generated explicit surface mesh utilizing modern hardware-tailored single precision ray tracing frameworks. We show that the overhead of mesh extraction and acceleration structure generation is compensated by the intersection performance for practical resolutions leading to an at least three times faster visibility calculation. We reveal the applicability of single precision ray tracing by attesting a sufficient angular resolution in conjunction with an integration method based on an up to twelve times subdivided icosahedron.

Properties of Silicon Ballistic Spin Fin-Based Field-Effect Transistors

We investigate the properties of ballistic fin-structured silicon spin field-effect transistors. The spin transistor suggested first by Datta and Das employs spin-orbit coupling to introduce the current modulation. The major contribution to the spin-orbit interaction in silicon films is of the Dresselhaus type due to the interface-induced inversion symmetry breaking. The subband structure in silicon confined systems is obtained with help of a two-band k·p model and is in good agreement with recent density functional calculations. It is demonstrated that fins with [100] orientation display a stronger modulation of the conductance as function of spin-orbit interaction and magnetic field and are thus preferred for practical realizations of silicon SpinFETs.

Using one-dimensional radiosity to model neutral particle flux in high aspect ratio holes

We present a computationally inexpensive one-dimensional method to model the neutral flux in high aspect ratio holes for three-dimensional plasma etching simulations. The benefit of our approach lies in the fact that the computational costs of a three-dimensional plasma etching simulation are, for the most part, determined by calculating the surface flux of the relevant species. We propose a one-dimensional radiosity model for the neutral flux by assuming an ideal cylindrical shape as well as ideal diffuse sources and surfaces. Our model reproduces the results obtained by a three-dimensional ray tracing simulation and is therefore suited to be used as a drop-in replacement for cylinder-like hole structures to speed up three-dimensional plasma etching simulations.

Transformation invariant local element size specification

Quality and size of mesh elements are important for optimizing the accuracy and convergence of mesh-based simulation processes. Often, a priori information, like internal material properties, of regions of interest is available, which can be used to locally specify the mesh element size for finding a good balance between the mesh resolution on the one hand and the runtime and memory performance on the other. In many applications, like the optimization of geometric parameters, multiple meshes of similar objects are required. Typical mesh element size specification methods, like scalar fields, are inflexible because of their dependence on the geometry of the object. To avoid the creation of a mesh element size specifications for each object manually, a specification method based on the objects topology rather than on its geometry, is needed. We tackle this problem by extending our meshing software ViennaMesh with a dynamic framework for locally specifying the size of mesh elements. Our approach aims for convenient utilization by using a XML-based configuration with support for arithmetic expressions. To achieve a high level of flexibility and reusability, this configuration can be specified based on the objects topology, for example interfaces between different material regions. Additionally, geometric parameters, like the radius of the circumsphere of the object, are provided and can be used to, e.g., scale the local mesh element size according to the total size of the object. As a result, our configuration method is invariant under large set transformations, especially deformations, of the object enabling a high level of geometry independence. We depict the practicability of our approach by providing examples for meshes generated with this element sizing framework and discussing a geometry optimization application.