Immo Huismann

Fast Static Condensation for the Helmholtz Equation in a Spectral-Element Discretization

Current research in computational fluid dynamics focuses on higher-order methods. These possess a more extensive coupling between degrees of freedom, resulting in a larger runtime per degree of freedom compared to low-order methods. This work tries to tackle this issue by combining the static condensation method with tensor-product and sum factorization, leading to a well-scaling solver for the Helmholtz equation.

Factorizing the factorization – a spectral-element solver for elliptic equations with linear operation count

Abstract The paper proposes a novel factorization technique for static condensation of a spectral-element discretization matrix that yields a linear operation count of just 13N multiplications for the residual evaluation, where N is the total number of unknowns. In comparison to previous work it saves a factor larger than 3 and outpaces unfactored variants for all polynomial degrees. Using the new technique as a building block for a preconditioned conjugate gradient method yields linear scaling of the runtime with N which is demonstrated for polynomial degrees from 2 to 32. This makes the spectral-element method cost effective even for low polynomial degrees. Moreover, the dependence of the iterative solution on the element aspect ratio is addressed, showing only a slight increase in the number of iterations for aspect ratios up to 128. Hence, the solver is very robust for practical applications.

CFDlang: High-level code generation for high-order methods in fluid dynamics

Numerical simulations continue to enable fast and enormous progress in science and engineering. Writing efficient numerical codes is a difficult challenge that encompasses a variety of tasks from designing the right algorithms to exploiting the full potential of a platforms architecture. Domain-specific languages (DSLs) can ease these tasks by offering the right abstractions for expressing numerical problems. With the aid of domain knowledge, efficient code can then be generated automatically from abstract expressions. In this work, we present the CFDlang DSL for expressing tensor operations that constitute the performance-critical code sections in a class of real numerical applications from fluid dynamics. We demonstrate that CFDlang can be used to generate code automatically that performs as well, if not better, than carefully hand-optimized code.

A Hardware/Software Stack for Heterogeneous Systems

Plenty of novel emerging technologies are being proposed and evaluated today, mostly at the device and circuit levels. It is unclear what the impact of different new technologies at the system level will be. What is clear, however, is that new technologies will make their way into systems and will increase the already high complexity of heterogeneous parallel computing platforms, making it ever so difficult to program them. This paper discusses a programming stack for heterogeneous systems that combines and adapts well-understood principles from different areas, including capability-based operating systems, adaptive application runtimes, dataflow programming models, and model checking. We argue why we think that these principles built into the stack and the interfaces among the layers will also be applicable to future systems that integrate heterogeneous technologies. The programming stack is evaluated on a tiled heterogeneous multicore.

Load Balancing for CPU-GPU Coupling in Computational Fluid Dynamics

This paper investigates static load balancing models for CPU-GPU coupling from a computational fluid dynamics perspective. While able to generate a benefit, traditional load balancing models are found to be too inaccurate to predict the runtime of a preconditioned conjugate gradient solver. Hence, an expanded model is derived that accounts for the multi-step nature of the solver, i.e. several communication barriers per iteration. It is able to predict the runtime to a margin of 5%, rendering CPU-GPU coupling better predictable so that load balancing can be improved substantially.

Using Semantics-aware Composition and Weaving for Multi-variant Progressive Parallelization

When writing parallel software for high performance computing, a common practice is to start from a sequential variant of a program that is consecutively enriched with parallelization directives. This process progressive parallelization has the advantage that, at every point in time, a correct version of the program exists. However, progressive parallelization leads to an entanglement of concerns, especially, if different variants of the same functional code have to be maintained and evolved concurrently. We propose orchestration style sheets (OSS) as a novel approach to separate parallelization concerns from problem-specific code by placing them in reusable style sheets, so that concerns for different platforms are always separated, and never lead to entanglement. A weaving process automatically generates platform-specific code for required target platforms, taking semantic properties of the source code into account. Based on a scientific-computing case study for fluid mechanics, we show that OSS are an adequate way to improve maintainability and reuse of Fortran code parallelized for several different platforms.