A performance study of general-purpose applications on graphics processors using CUDA

Graphics processors (GPUs) provide a vast number of simple, data-parallel, deeply multithreaded cores and high memory bandwidths. GPU architectures are becoming increasingly programmable, offering the potential for dramatic speedups for a variety of general-purpose applications compared to contemporary general-purpose processors (CPUs). This paper uses NVIDIA’s C-like CUDA language and an engineering sample of their recently introduced GTX 260 GPU to explore the effectiveness of GPUs for a variety of application types, and describes some specific coding idioms that improve their performance on the GPU. GPU performance is compared to both single-core and multicore CPU performance, with multicore CPU implementations written using OpenMP. The paper also discusses advantages and inefficiencies of the CUDA programming model and some desirable features that might allow for greater ease of use and also more readily support a larger body of applications.     

Integrated modeling, finite-element analysis, and engineering design for thin-shell structures using subdivision

Many engineering design applications require geometric modeling and mechanical simulation of thin flexible structures, such as those found in the automotive and aerospace industries. Traditionally, geometric modeling, mechanical simulation, and engineering design are treated as separate modules requiring different methods and representations. Due to the incompatibility of the involved representations the transition from geometric modeling to mechanical simulation, as well as in the opposite direction, requires substantial effort. However, for engineering design purposes efficient transition between geometric modeling and mechanical simulation is essential. We propose the use of subdivision surfaces as a common foundation for modeling, simulation, and design in a unified framework. Subdivision surfaces provide a flexible and efficient tool for arbitrary topology free-form surface modeling, avoiding many of the problems inherent in traditional spline patch based approaches. The underlying basis functions are also ideally suited for a finite-element treatment of the so-called thin-shell equations, which describe the mechanical behavior of the modeled structures. The resulting solvers are highly scalable, providing an efficient computational foundation for design exploration and optimization. We demonstrate our claims with several design examples, showing the versatility and high accuracy of the proposed method.     

Accuracy enhancement for non-isoparametric finite-element simulations in curved domains; application to fluid flow

Among a few known techniques the isoparametric version of the finite element method for meshes consisting of curved triangles or tetrahedra is the one most widely employed to solve PDEs with essential conditions prescribed on curved boundaries. It allows to recover optimal approximation properties that hold for elements of order greater than one in the energy norm for polytopic domains. However, besides a geometric complexity, this technique requires the manipulation of rational functions and the use of numerical integration. We consider a simple alternative to deal with Dirichlet boundary conditions that bypasses these drawbacks, without eroding qualitative approximation properties. In the present work we first recall the main principle this technique is based upon, by taking as a model the solution of the Poisson equation with quadratic Lagrange finite elements. Then we show that it extends very naturally to viscous incompressible flow problems. Although the technique applies to any higher order velocity–pressure pairing, as an illustration a thorough study thereof is conducted in the framework of the Stokes system solved by the classical Taylor–Hood method.