Related papers: Exponential Integrators on Graphic Processing Unit…
The simulation of heat flow through heterogeneous material is important for the design of structural and electronic components. Classical analytical solutions to the heat equation PDE are not known for many such domains, even those having…
The strategy of using CUDA-compatible GPUs as a parallel computation solution to improve the performance of programs has been more and more widely approved during the last two years since the CUDA platform was released. Its benefit extends…
Future experiments in high-energy physics will pose stringent requirements to computing, in particular to real-time data processing. As an example, the CBM experiment at FAIR Germany intends to perform online data selection exclusively in…
In this work, we consider the solution of boundary integral equations by means of a scalable hierarchical matrix approach on clusters equipped with graphics hardware, i.e. graphics processing units (GPUs). To this end, we extend our…
Immersed boundary methods (IBMs) facilitate the simulation of flows around stationary, moving, and deforming bodies on Cartesian grids. However, extending these simulations to the large grid sizes required for realistic flow problems…
Hybrid computational architectures based on the joint power of Central Processing Units and Graphic Processing Units (GPUs) are becoming popular and powerful hardware tools for a wide range of simulations in biology, chemistry, engineering,…
Motivated by the Hodgkin-Huxley model of neuronal dynamics, we study explicit numerical integrators for "conditionally linear" systems of ordinary differential equations. We show that splitting and composition methods, when applied to the…
In the present paper we consider numerical methods to solve the discrete Schr\"odinger equation with a time dependent Hamiltonian (motivated by problems encountered in the study of spin systems). We will consider both short-range…
Stencil algorithms on regular lattices appear in many fields of computational science, and much effort has been put into optimized implementations. Such activities are usually not guided by performance models that provide estimates of…
We describe a method for parallelizing the lexicographic enumeration algorithm for the factorization set of an element in a numerical semigroup via bounds. This enables the use of GPU and distributed computing methods. We provide a CUDA…
Stencil computations consume a major part of runtime in many scientific simulation codes. As prototypes for this class of algorithms we consider the iterative Jacobi and Gauss-Seidel smoothers and aim at highly efficient parallel…
GPUs have significantly accelerated first-order methods for large-scale optimization, especially in continuous optimization. However, this success has not transferred cleanly to problems with discrete variables, combinatorial structure, and…
In this paper, we further develop a family of parallel time integrators known as Revisionist Integral Deferred Correction methods (RIDC) to allow for the semi-implicit solution of time dependent PDEs. Additionally, we show that our…
Finite element schemes based on discontinuous Galerkin methods possess features amenable to massively parallel computing accelerated with general purpose graphics processing units (GPUs). However, the computational performance of such…
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…
In this era of diverse and heterogeneous computer architectures, the programmability issues, such as productivity and portable efficiency, are crucial to software development and algorithm design. One way to approach the problem is to step…
We demonstrate a high-performance vendor-agnostic method for massively parallel solving of ensembles of ordinary differential equations (ODEs) and stochastic differential equations (SDEs) on GPUs. The method is integrated with a widely used…
We present algorithms for computing strongly singular and near-singular surface integrals over curved triangular patches, based on singularity subtraction, the continuation approach, and transplanted Gauss quadrature. We demonstrate the…
We present a higher-order finite volume method for solving elliptic PDEs with jump conditions on interfaces embedded in a 2D Cartesian grid. Second, fourth, and sixth order accuracy is demonstrated on a variety of tests including problems…
The focus of my PhD thesis is on exploring parallel approaches to efficiently solve problems modeled by constraints and presenting a new proposal. Current solvers are very advanced; they are carefully designed to effectively manage the…