arXiv subjects

Arturo Vargas

Publications and source records attributed to Arturo Vargas.

7 recordsLinked to original sources

arXiv2025

Understanding Power and Energy Utilization in Large Scale Production Physics Simulation Codes

Power is an often-cited reason for the move to advanced architectures on the path to Exascale computing. This is due to practical considerations related to delivering enough power to successfully site and operate these machines, as well as concerns about energy usage while running large simulations. Since obtaining accurate power measurements can be challenging, it may be tempting to use the processor thermal design power (TDP) as a surrogate due to its simplicity and availability. However, TDP is not indicative of typical power usage while running simulations. Using commodity and advanced technology systems at Lawrence Livermore and Sandia National Labs, we performed a series of experiments to measure power and energy usage in running simulation codes. These experiments indicate that large scale Lawrence Livermore simulation codes are significantly more efficient than a simple processor TDP model might suggest.

cs.DC↗

arXiv2021

Matrix-free approaches for GPU acceleration of a high-order finite element hydrodynamics application using MFEM, Umpire, and RAJA

With the introduction of advanced heterogeneous computing architectures based on GPU accelerators, large-scale production codes have had to rethink their numerical algorithms and incorporate new programming models and memory management strategies in order to run efficiently on the latest supercomputers. In this work we discuss our co-design strategy to address these challenges and achieve performance and portability with MARBL, a next-generation multi-physics code in development at Lawrence Livermore National Laboratory. We present a two-fold approach, wherein new hardware is used to motivate both new algorithms and new abstraction layers, resulting in a single source application code suitable for a variety of platforms. Focusing on MARBL's ALE hydrodynamics package, we demonstrate scalability on different platforms and highlight that many of our innovations have been contributed back to open-source software libraries, such as MFEM (finite element algorithms) and RAJA (kernel abstractions).

cs.MS↗

arXiv2021

GPU Algorithms for Efficient Exascale Discretizations

In this paper we describe the research and development activities in the Center for Efficient Exascale Discretization within the US Exascale Computing Project, targeting state-of-the-art high-order finite-element algorithms for high-order applications on GPU-accelerated platforms. We discuss the GPU developments in several components of the CEED software stack, including the libCEED, MAGMA, MFEM, libParanumal, and Nek projects. We report performance and capability improvements in several CEED-enabled applications on both NVIDIA and AMD GPU systems.

cs.DC↗

arXiv2018

Leapfrog time-stepping for Hermite methods

We introduce Hermite-leapfrog methods for first order wave systems. The new Hermite-leapfrog methods pair leapfrog time-stepping with the Hermite methods of Goodrich and co-authors. The new schemes stagger field variables in both time and space and are high-order accurate. We provide a detailed description of the method and demonstrate that the method conserves variable quantities in one-space dimension. Higher dimensional versions of the method are constructed via a tensor product construction. Numerical evidence and rigorous analysis in one space dimension establish stability and high-order convergence. Experiments demonstrating efficient implementations on a graphics processing unit are also presented.

math.NA↗

arXiv2018

Hermite Methods for the Scalar Wave Equation

Arbitrary order dissipative and conservative Hermite methods for the scalar wave equation achieving $\mathcal{O}(2m)$ orders of accuracy using $\mathcal{O}(m^d)$ degrees of freedom per node in $d$ dimensions are presented. Stability and error analyses as well as implementation strategies for accelerators are also given.

math.NA↗

arXiv2016

GPU Acceleration of Hermite Methods for the Simulation of Wave Propagation

The Hermite methods of Goodrich, Hagstrom, and Lorenz (2006) use Hermite interpolation to construct high order numerical methods for hyperbolic initial value problems. The structure of the method has several favorable features for parallel computing. In this work, we propose algorithms that take advantage of the many-core architecture of Graphics Processing Units. The algorithm exploits the compact stencil of Hermite methods and uses data structures that allow for efficient data load and stores. Additionally the highly localized evolution operator of Hermite methods allows us to combine multi-stage time-stepping methods within the new algorithms incurring minimal accesses of global memory. Using a scalar linear wave equation, we study the algorithm by considering Hermite interpolation and evolution as individual kernels and alternatively combined them into a monolithic kernel. For both approaches we demonstrate strategies to increase performance. Our numerical experiments show that although a two kernel approach allows for better performance on the hardware, a monolithic kernel can offer a comparable time to solution with less global memory usage.

math.NA↗

arXiv2015

Variations on Hermite methods for wave propagation

Hermite methods, as introduced by Goodrich et al., combine Hermite interpolation and staggered (dual) grids to produce stable high order accurate schemes for the solution of hyperbolic PDEs. We introduce three variations of this Hermite method which do not involve time evolution on dual grids. Computational evidence is presented regarding stability, high order convergence, and dispersion/dissipation properties for each new method. Hermite methods may also be coupled to discontinuous Galerkin (DG) methods for additional geometric flexibility. An example illustrates the simplification of this coupling of this coupling for the Hermite methods.

math.NA↗