1,077 research outputs found
Towards a Mini-App for Smoothed Particle Hydrodynamics at Exascale
The smoothed particle hydrodynamics (SPH) technique is a purely Lagrangian
method, used in numerical simulations of fluids in astrophysics and
computational fluid dynamics, among many other fields. SPH simulations with
detailed physics represent computationally-demanding calculations. The
parallelization of SPH codes is not trivial due to the absence of a structured
grid. Additionally, the performance of the SPH codes can be, in general,
adversely impacted by several factors, such as multiple time-stepping,
long-range interactions, and/or boundary conditions. This work presents
insights into the current performance and functionalities of three SPH codes:
SPHYNX, ChaNGa, and SPH-flow. These codes are the starting point of an
interdisciplinary co-design project, SPH-EXA, for the development of an
Exascale-ready SPH mini-app. To gain such insights, a rotating square patch
test was implemented as a common test simulation for the three SPH codes and
analyzed on two modern HPC systems. Furthermore, to stress the differences with
the codes stemming from the astrophysics community (SPHYNX and ChaNGa), an
additional test case, the Evrard collapse, has also been carried out. This work
extrapolates the common basic SPH features in the three codes for the purpose
of consolidating them into a pure-SPH, Exascale-ready, optimized, mini-app.
Moreover, the outcome of this serves as direct feedback to the parent codes, to
improve their performance and overall scalability.Comment: 18 pages, 4 figures, 5 tables, 2018 IEEE International Conference on
Cluster Computing proceedings for WRAp1
An extreme-scale implicit solver for complex PDEs: highly heterogeneous flow in earth's mantle
Mantle convection is the fundamental physical process within earth's interior responsible for the thermal and geological evolution of the planet, including plate tectonics. The mantle is modeled as a viscous, incompressible, non-Newtonian fluid. The wide range of spatial scales, extreme variability and anisotropy in material properties, and severely nonlinear rheology have made global mantle convection modeling with realistic parameters prohibitive. Here we present a new implicit solver that exhibits optimal algorithmic performance and is capable of extreme scaling for hard PDE problems, such as mantle convection. To maximize accuracy and minimize runtime, the solver incorporates a number of advances, including aggressive multi-octree adaptivity, mixed continuous-discontinuous discretization, arbitrarily-high-order accuracy, hybrid spectral/geometric/algebraic multigrid, and novel Schur-complement preconditioning. These features present enormous challenges for extreme scalability. We demonstrate that---contrary to conventional wisdom---algorithmically optimal implicit solvers can be designed that scale out to 1.5 million cores for severely nonlinear, ill-conditioned, heterogeneous, and anisotropic PDEs
Modelling solid/fluid interactions in hydrodynamic flows: a hybrid multiscale approach
With the advent of high performance computing (HPC), we can
simulate nature at time and length scales that we could only dream of a few
decades ago. Through the development of theory and numerical methods in
the last fifty years, we have at our disposal a plethora of mathematical and
computational tools to make powerful predictions about the world which
surrounds us. From quantum methods like Density Functional Theory
(DFT); going through atomistic methods such as Molecular Dynamics (MD)
and Monte Carlo (MC), right up to more traditional macroscopic techniques
based on Partial Differential Equations (PDEs) discretization like the Finite
Element Method (FEM) or Finite Volume Method (FVM), which are
respectively, the foundation of computational Structural Analysis and
Computational Fluid Dynamics (CFD). Many modern scientific computing
challenges in physics stem from combining appropriately two or more of
these methods, in order to tackle problems that could not be solved
otherwise using just one of them alone. This is known as multi-scale
modeling, which aims to achieve a trade-off between computational cost and
accuracy by combining two or more physical models at different scales.
In this work, a multi-scale domain decomposition technique based on
coupling MD and CFD methods, has been developed to make affordable the
study of slip and friction, with atomistic detail, at length scales otherwise
impossible by fully atomistic methods alone. A software framework has been
developed to facilitate the execution of this particular kind of simulations on
HPC clusters. This have been possible by employing the in-house developed
CPL_LIBRARY software library, which provides key functionality to implement
coupling through domain decomposition.Open Acces
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Global convection in Earth's mantle : advanced numerical methods and extreme-scale simulations
The thermal convection of rock in Earth's mantle and associated plate tectonics are modeled by nonlinear incompressible Stokes and energy equations. This dissertation focuses on the development of advanced, scalable linear and nonlinear solvers for numerical simulations of realistic instantaneous mantle flow, where we must overcome several computational challenges. The most notable challenges are the severe nonlinearity, heterogeneity, and anisotropy due to the mantle's rheology as well as a wide range of spatial scales and highly localized features. Resolving the crucial small scale features efficiently necessitates adaptive methods, while computational results greatly benefit from a high accuracy per degree of freedom and local mass conservation. Consequently, the discretization of Earth's mantle is carried out by high-order finite elements on aggressively adaptively refined hexahedral meshes with a continuous, nodal velocity approximation and a discontinuous, modal pressure approximation. These velocity--pressure pairings yield optimal asymptotic convergence rates of the finite element approximation to the infinite-dimensional solution with decreasing mesh element size, are inf-sup stable on general, non-conforming hexahedral meshes with "hanging nodes,'' and have the advantage of preserving mass locally at the element level due to the discontinuous pressure. However, because of the difficulties cited above and the desired accuracy, the large implicit systems to be solved are extremely poorly conditioned and sophisticated linear and nonlinear solvers including powerful preconditioning techniques are required. The nonlinear Stokes system is solved using a grid continuation, inexact Newton--Krylov method. We measure the residual of the momentum equation in the H⁻¹-norm for backtracking line search to avoid overly conservative update steps that are significantly reduced from one. The Newton linearization is augmented by a perturbation of a highly nonlinear term in mantle's rheology, resulting in dramatically improved nonlinear convergence. We present a new Schur complement-based Stokes preconditioner, weighted BFBT, that exhibits robust fast convergence for Stokes problems with smooth but highly varying (up to 10 orders of magnitude) viscosities, optimal algorithmic scalability with respect to mesh refinement, and only a mild dependence on the polynomial order of high-order finite element discretizations. In addition, we derive theoretical eigenvalue bounds to prove spectral equivalence of our inverse Schur complement approximation. Finally, we present a parallel hybrid spectral--geometric--algebraic multigrid (HMG) to approximate the inverses of the Stokes system's viscous block and variable-coefficient pressure Poisson operators within weighted BFBT. Building on the parallel scalability of HMG, our Stokes solver demonstrates excellent parallel scalability to 1.6 million CPU cores without sacrificing algorithmic optimality.Computational Science, Engineering, and Mathematic
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