arXiv subjects

Daniel Arndt

Publications and source records attributed to Daniel Arndt.

At least 19 recordsLinked to original sources

arXiv2025

The ArborX library: version 2.0

This paper provides an overview of the 2.0 release of the ArborX library, a performance portable geometric search library based on Kokkos. We describe the major changes in ArborX 2.0 including a new interface for the library to support a wider range of user problems, new search data structures (brute force, distributed), support for user functions to be executed on the results (callbacks), and an expanded set of the supported algorithms (ray tracing, clustering).

cs.DC↗

arXiv2024

Advances in ArborX to support exascale applications

ArborX is a performance portable geometric search library developed as part of the Exascale Computing Project (ECP). In this paper, we explore a collaboration between ArborX and a cosmological simulation code HACC. Large cosmological simulations on exascale platforms encounter a bottleneck due to the in-situ analysis requirements of halo finding, a problem of identifying dense clusters of dark matter (halos). This problem is solved by using a density-based DBSCAN clustering algorithm. With each MPI rank handling hundreds of millions of particles, it is imperative for the DBSCAN implementation to be efficient. In addition, the requirement to support exascale supercomputers from different vendors necessitates performance portability of the algorithm. We describe how this challenge problem guided ArborX development, and enhanced the performance and the scope of the library. We explore the improvements in the basic algorithms for the underlying search index to improve the performance, and describe several implementations of DBSCAN in ArborX. Further, we report the history of the changes in ArborX and their effect on the time to solve a representative benchmark problem, as well as demonstrate the real world impact on production end-to-end cosmology simulations.

cs.DC↗

arXiv2021

Fast tree-based algorithms for DBSCAN for low-dimensional data on GPUs

DBSCAN is a well-known density-based clustering algorithm to discover arbitrary shape clusters. While conceptually simple in serial, the algorithm is challenging to efficiently parallelize on manycore GPU architectures. Common pitfalls, such as asynchronous range query calls, result in high thread execution divergence in many implementations. In this paper, we propose a new framework for GPU-accelerated DBSCAN, and describe two tree-based algorithms within that framework. Both algorithms fuse the search for neighbors with updating cluster information, but differ in their treatment of dense regions of the data. We show that the time taken to compute clusters is at most twice that of determination of the neighbors. We compare the proposed algorithms with existing CPU and GPU implementations, and demonstrate their competitiveness and performance using a fast traversal structure (bounding volume hierarchy) for low dimensional data. We also show that the memory usage can be reduced by processing object neighbors dynamically without storing them.

cs.DC↗

arXiv2020

The deal.II finite element library: design, features, and insights

deal.II is a state-of-the-art finite element library focused on generality, dimension-independent programming, parallelism, and extensibility. Herein, we outline its primary design considerations and its sophisticated features such as distributed meshes, $hp$-adaptivity, support for complex geometries, and matrix-free algorithms. But deal.II is more than just a software library: It is also a diverse and worldwide community of developers and users, as well as an educational platform. We therefore also discuss some of the technical and social challenges and lessons learned in running a large community software project over the course of two decades.

cs.MS↗

arXiv2019

Fast Tensor Product Schwarz Smoothers for High-Order Discontinuous Galerkin Methods

In this article, we discuss the efficient implementation of powerful domain decomposition smoothers for multigrid methods for high order discontinuous Galerkin (DG) finite element methods. In particular, we study the inversion of matrices associated to mesh cells and to the patches around a vertex, respectively, in order to obtain fast local solvers for additive and multiplicative subspace correction methods. The effort of inverting local matrices for tensor product polynomials of degree $k$ is reduced from $\mathcal O(k^{3d})$ to $\mathcal O(dk^{d+1})$ by exploiting the separability of the differential operator and resulting low rank representation of its inverse as a prototype for more general low rank representations.

math.NA↗

arXiv2019

A matrix-free approach for finite-strain hyperelastic problems using geometric multigrid

The performance of finite element solvers on modern computer architectures is typically memory bound for sufficiently large problems. The main cause for this is that loading matrix elements from RAM into CPU cache is significantly slower than performing the arithmetic operations when solving the problem. In order to improve the performance of iterative solvers within the high-performance computing context, so-called matrix-free methods are widely adopted in the fluid mechanics community, where matrix-vector products are computed on-the-fly. To date, there have been few (if any) assessments into the applicability of the matrix-free approach to problems in solid mechanics. In this work, we perform an initial investigation on the application of the matrix-free approach to problems in quasi-static finite-strain hyperelasticity to determine whether it is viable for further extension. Specifically, we study different numerical implementations of the finite element tangent operator, and determine whether generalized methods of incorporating complex constitutive behavior might be feasible. In order to improve the convergence behavior of iterative solvers, we also propose a method by which to construct level tangent operators and employ them to define a geometric multigrid preconditioner. The performance of the matrix-free operator and the geometric multigrid preconditioner is compared to the matrix-based implementation with an algebraic multigrid preconditioner on a single node for a representative numerical example of a heterogeneous hyperelastic material in two and three dimensions. We conclude that the application of matrix-free methods to finite-strain solid mechanics is promising, and that is it possible to develop numerically efficient implementations that are independent of the hyperelastic constitutive law.

math.NA↗

arXiv2018

A C1-mapping based on finite elements on quadrilateral and hexahedral meshes

Finite elements of higher continuity, say conforming in $H^2$ instead of $H^1$, require a mapping from reference cells to mesh cells which is continuously differentiable across cell interfaces. In this article, we propose an algorithm to obtain such mappings given a topologically regular mesh in the standard format of vertex coordinates and a description of the boundary. A variant of the algorithm with orthogonal edges in each vertex is proposed. We introduce necessary modifications in the case of adaptive mesh refinement with nonconforming edges. Furthermore, we discuss efficient storage of the necessary data.

math.NA↗

arXiv2016

Quasi-Optimal Error Estimates for the Incompressible Navier-Stokes Problem Discretized by Finite Element Methods and Pressure-Correction Projection with Velocity Stabilization

We consider error estimates for the fully discretized instationary Navier-Stokes problem. For the spatial approximation we use conforming inf-sup stable finite element methods in conjunction with grad-div and local projection stabilization acting on the streamline derivative. For the temporal discretization a pressure-correction projection algorithm based on BDF2 is used. We can show quasi-optimal rates of convergence with respect to time and spatial discretization for all considered error measures. Some of the error estimates are quasi-robust with respect to the Reynolds number.

math.NA↗

arXiv2004

Chiral Perturbation Theory on the Lattice and its Applications

Chiral perturbation theory (CPT), the low-energy effective theory of QCD, can be used to describe QCD observables in the low-energy region in a model-independent way. At any given order in the chiral expansion, CPT introduces a finite number of parameters that encode the short-distance physics and that must be determined from experiment or numerical lattice QCD simulations. In this thesis, we calculate a number of hadronic observables in the quenched and partially quenched versions of CPT: Chiral corrections to B^(*) --> D^(*) at zero recoil are investigated in quenched CPT. We study in detail the charge radii of the meson and baryon octets, electromagnetic properties of the baryon decuplet, and the baryon decuplet to octet electromagnetic transitions in both, quenched and partially quenched CPT. We further show how effects due to the finite size of the lattice can be accounted for in heavy meson CPT and calculate, as explicit examples, neutral B meson mixing and the heavy-light meson decay constants. We also demonstrate how one can account for effects due to finite lattice spacing in the low-energy theories, considering as an example electromagnetic meson and baryon properties. The results of our calculations are crucial to extrapolate quenched and partially quenched lattice data from the heavier light quark masses used on the lattice to the physical values.

hep-lat↗

arXiv2004

Heavy meson chiral perturbation theory in finite volume

We study finite volume effects in heavy quark systems in the framework of heavy meson chiral perturbation theory for full, quenched, and partially quenched QCD. A novel feature of this investigation is the role played by the scales Delta and delta_s, where Delta is the mass difference between the heavy-light vector and pseudoscalar mesons of the same quark content, and delta_s is the mass difference due to light flavour SU(3) breaking. The primary conclusion of this work is that finite volume effects arising from the propagation of Goldstone particles in the effective theory can be altered by the presence of these scales. Since Delta varies significantly with the heavy quark mass, these volume effects can be amplified in both heavy and light quark mass extrapolations (interpolations). As an explicit example, we present results for B parameters of neutral B meson mixing matrix elements and heavy-light decay constants to one-loop order in finite volume heavy meson chiral perturbation theory for full, quenched, and N_f=2+1 partially quenched QCD. Our calculation shows that for high-precision determinations of the phenomenologically interesting SU(3) breaking ratios, finite volume effects are significant in quenched and not negligible in partially quenched QCD, although they are generally small in full QCD.

hep-lat↗

arXiv2004

Hadronic Electromagnetic Properties at Finite Lattice Spacing

Electromagnetic properties of the octet mesons as well as the octet and decuplet baryons are augmented in quenched and partially quenched chiral perturbation theory to include O(a) corrections due to lattice discretization. We present the results for the SU(3) flavor group in the isospin limit as well as the results for SU(2) flavor with non-degenerate quarks. These corrections will be useful for extrapolation of lattice calculations using Wilson valence and sea quarks, as well as calculations using Wilson sea quarks and Ginsparg-Wilson valence quarks.

hep-lat↗

arXiv2003

Charge Radii of the Meson and Baryon Octets in Quenched and Partially Quenched Chiral Perturbation Theory

We calculate the electric charge radii of the SU(3) pseudoscalar mesons and the SU(3) octet baryons in quenched and partially quenched chiral perturbation theory. We work in the isospin limit, up to next-to-leading order in the chiral expansion, and to leading order in the heavy baryon expansion. The results are necessary for the extrapolation of future lattice calculations of meson and baryon charge radii. We also derive expressions for the nucleon and pion charge radii in SU(2) flavor away from the isospin limit.

hep-lat↗

arXiv2003

Baryon Decuplet to Octet Electromagnetic Transitions in Quenched and Partially Quenched Chiral Perturbation Theory

We calculate baryon decuplet to octet electromagnetic transition form factors in quenched and partially quenched chiral perturbation theory. We work in the isospin limit of SU(3) flavor, up to next-to-leading order in the chiral expansion, and to leading order in the heavy baryon expansion. Our results are necessary for proper extrapolation of lattice calculations of these transitions. We also derive expressions for the case of SU(2) flavor away from the isospin limit.

hep-lat↗

arXiv2003

Electromagnetic Properties of the Baryon Decuplet in Quenched and Partially Quenched Chiral Perturbation Theory

We calculate electromagnetic properties of the decuplet baryons in quenched and partially quenched chiral perturbation theory. We work at next-to-leading order in the chiral expansion, leading order in the heavy baryon expansion, and obtain expressions for the magnetic moments, charge radii, and electric quadrupole moments. The quenched calculation is shown to be pathological since only quenched chiral singularities are present at this order. We present the partially quenched results for both the SU(2) and SU(3) flavor groups and use the isospin limit in the latter. These results are necessary for proper extrapolation of lattice calculations of decuplet electromagnetic properties.

hep-lat↗

arXiv2003

The Lambda_Q-Lambda_Q Potential

Lattice QCD simulations of the potential between two baryons, each containing a heavy quark and two light quarks, such as the Lambda_Q-Lambda_Q potential, will provide insight into the nucleon-nucleon interaction. As one-pion exchange does not contribute to the Lambda_Q-Lambda_Q potential, the long-distance behavior is dominated by physics that contributes to the intermediate-range attraction between two nucleons. We compute the leading long-distance contributions to the Lambda_Q-Lambda_Q potential in QCD and in partially-quenched QCD in the low-energy effective field theory.

nucl-th↗

arXiv2003

Saxion Emission from SN1987A

We study the possibility of emission of the saxion, a superpartner of the axion, from SN1987A. The fact that the observed neutrino pulse from SN1987A is in excellent agreement with the current theory of supernovae places a strong bound on the energy loss into any non-standard model channel, therefore enabling bounds to be placed on the decay constant, f_a, of a light saxion. The low-energy coupling of the saxion, which couples at high energies to the QCD gauge field strength, is expected to be enhanced from QCD scaling, making it interesting to investigate if the saxion could place stronger bounds on f_a than the axion itself. Moreover, since the properties of the saxion are determined by f_a, a constraint on this parameter can be translated into a constraint on the supersymmetry breaking scale. We find that the bound on f_a from saxion emission is comparable with the one derived from axion emission due to a cancellation of leading-order terms in the soft-radiation expansion.

hep-ph↗

arXiv2002

Chiral 1/M^2 corrections to B^() -> D^() at Zero Recoil in Quenched Chiral Perturbation Theory

Heavy quark effective theory can be used to calculate the values of the semileptonic B^(*) -> D^(*) decays in the limit that the heavy quark masses are infinite. We calculate the lowest order chiral corrections, which are of O(1/M^2), from the breaking of heavy quark symmetry at the zero recoil point in quenched chiral perturbation theory. These results will aid in the extrapolation of quenched lattice calculations from the light quark masses used on the lattice down to the physical ones.

hep-lat↗

arXiv2001

How a quark-gluon plasma phase modifies the bounds on extra dimensions from SN 1987a

The shape of the neutrino pulse from the supernova SN1987a provides one of the most stringent constraints on the size of large, compact, "gravity-only" extra dimensions. Previously, calculations have been carried out for a newly-born proto-neutron star with a temperature of about 50 MeV at nuclear matter density. It is arguable that, due to the extreme conditions in the interior of the star, matter might be a quark-gluon plasma, where the relevant degrees of freedom are quarks and gluons rather than nucleons. We consider an energy-loss scenario where seconds after rebounce the core of the star consists of a hot and dense quark-gluon plasma. Adopting a simplified model of the plasma we derive the necessary energy-loss formulae in the soft-radiation limit. The emissivity is found to be comparable to the one for nuclear matter and bounds on the radius of extra dimensions are similar to those found previously from nuclear matter calculations.

nucl-th↗