scholarly journals magritte, a modern software library for 3D radiative transfer – II. Adaptive ray-tracing, mesh construction, and reduction

2020 ◽  
Vol 499 (4) ◽  
pp. 5194-5204
Author(s):  
Frederik De Ceuster ◽  
Jan Bolte ◽  
Ward Homan ◽  
Silke Maes ◽  
Jolien Malfait ◽  
...  
Keyword(s):  
Radiative Transfer ◽  
Ray Tracing ◽  
Adaptive Mesh Refinement ◽  
Computational Cost ◽  
Adaptive Mesh ◽  
Significant Loss ◽  
Discretization Scheme ◽  
Software Library ◽  
Particle Hydrodynamics ◽  
Order Of Magnitude

ABSTRACT Radiative transfer is a notoriously difficult and computationally demanding problem. Yet, it is an indispensable ingredient in nearly all astrophysical and cosmological simulations. Choosing an appropriate discretization scheme is a crucial part of the simulation, since it not only determines the direct memory cost of the model but also largely determines the computational cost and the achievable accuracy. In this paper, we show how an appropriate choice of directional discretization scheme as well as spatial model mesh can help alleviate the computational cost, while largely retaining the accuracy. First, we discuss the adaptive ray-tracing scheme implemented in our 3D radiative transfer library magritte, that adapts the rays to the spatial mesh and uses a hierarchical directional discretization based on healpix. Second, we demonstrate how the free and open-source software library gmsh can be used to generate high-quality meshes that can be easily tailored for magritte. In particular, we show how the local element size distribution of the mesh can be used to optimize the sampling of both analytically and numerically defined models. Furthermore, we show that when using the output of hydrodynamics simulations as input for a radiative transfer simulation, the number of elements in the input model can often be reduced by an order of magnitude, without significant loss of accuracy in the radiation field. We demonstrate this for two models based on a hierarchical octree mesh resulting from adaptive mesh refinement, as well as two models based on smoothed particle hydrodynamics data.

scholarly journals Accelerating numerical wave propagation using wavefield adapted meshes. Part I: forward and adjoint modelling

2020 ◽  
Vol 221 (3) ◽  
pp. 1580-1590 ◽  
Author(s):  
M van Driel ◽  
C Boehm ◽  
L Krischer ◽  
M Afanasiev
Keyword(s):  
Wave Propagation ◽  
Adaptive Mesh Refinement ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Model Space ◽  
Adaptive Mesh ◽  
Order Of Magnitude ◽  
Speed Up ◽  
Adjoint Modelling ◽  
The Waves

SUMMARY An order of magnitude speed-up in finite-element modelling of wave propagation can be achieved by adapting the mesh to the anticipated space-dependent complexity and smoothness of the waves. This can be achieved by designing the mesh not only to respect the local wavelengths, but also the propagation direction of the waves depending on the source location, hence by anisotropic adaptive mesh refinement. Discrete gradients with respect to material properties as needed in full waveform inversion can still be computed exactly, but at greatly reduced computational cost. In order to do this, we explicitly distinguish the discretization of the model space from the discretization of the wavefield and derive the necessary expressions to map the discrete gradient into the model space. While the idea is applicable to any wave propagation problem that retains predictable smoothness in the solution, we highlight the idea of this approach with instructive 2-D examples of forward as well as inverse elastic wave propagation. Furthermore, we apply the method to 3-D global seismic wave simulations and demonstrate how meshes can be constructed that take advantage of high-order mappings from the reference coordinates of the finite elements to physical coordinates. Error level and speed-ups are estimated based on convergence tests with 1-D and 3-D models.

scholarly journals Convergence of SPH and AMR simulations

2010 ◽  
Vol 6 (S270) ◽  
pp. 429-432
Author(s):  
David A. Hubber ◽  
Sam A. E. G. Falle ◽  
Simon P. Goodwin
Keyword(s):  
Smoothed Particle Hydrodynamics ◽  
Thin Shell ◽  
Adaptive Mesh Refinement ◽  
Adaptive Mesh ◽  
Helmholtz Instability ◽  
Non Linear ◽  
Particle Hydrodynamics ◽  
First Results ◽  
Order Of Magnitude ◽  
Smoothed Particle

AbstractWe present the first results of a large suite of convergence tests between Adaptive Mesh Refinement (AMR) Finite Difference Hydrodynamics and Smoothed Particle Hydrodynamics (SPH) simulations of the non-linear thin shell instability and the Kelvin-Helmholtz instability. We find that the two methods converge in the limit of high resolution and accuracy. AMR and SPH simulations of the non-linear thin shell instability converge with each other with standard algorithms and parameters. The Kelvin-Helmholtz instability in SPH requires both an artificial conductivity term and a kernel with larger compact support and more neighbours (e.g. the quintic kernel) in order converge with AMR. For purely hydrodynamical problems, SPH simulations take an order of magnitude longer than the grid code when converged.

scholarly journals AMReX: Block-structured adaptive mesh refinement for multiphysics applications

2021 ◽  
pp. 109434202110228
Author(s):  
Weiqun Zhang ◽  
Andrew Myers ◽  
Kevin Gott ◽  
Ann Almgren ◽  
John Bell
Keyword(s):  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Computational Cost ◽  
Adaptive Mesh ◽  
Uniform Mesh ◽  
Physical Processes ◽  
Structured Adaptive Mesh Refinement ◽  
Core Elements ◽  
Accelerator Design ◽  
Block Structured

Block-structured adaptive mesh refinement (AMR) provides the basis for the temporal and spatial discretization strategy for a number of Exascale Computing Project applications in the areas of accelerator design, additive manufacturing, astrophysics, combustion, cosmology, multiphase flow, and wind plant modeling. AMReX is a software framework that provides a unified infrastructure with the functionality needed for these and other AMR applications to be able to effectively and efficiently utilize machines from laptops to exascale architectures. AMR reduces the computational cost and memory footprint compared to a uniform mesh while preserving accurate descriptions of different physical processes in complex multiphysics algorithms. AMReX supports algorithms that solve systems of partial differential equations in simple or complex geometries and those that use particles and/or particle–mesh operations to represent component physical processes. In this article, we will discuss the core elements of the AMReX framework such as data containers and iterators as well as several specialized operations to meet the needs of the application projects. In addition, we will highlight the strategy that the AMReX team is pursuing to achieve highly performant code across a range of accelerator-based architectures for a variety of different applications.

scholarly journals CPU Isosurface Ray Tracing of Adaptive Mesh Refinement Data

2019 ◽  
Vol 25 (1) ◽  
pp. 1142-1151 ◽  
Author(s):  
Feng Wang ◽  
Ingo Wald ◽  
Qi Wu ◽  
Will Usher ◽  
Chris R. Johnson
Keyword(s):  
Ray Tracing ◽  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Adaptive Mesh

scholarly journals MOLECULAR STATICS SIMULATION OF NANOINDENTATION USING ADAPTIVE QUASICONTINUUM METHOD

2018 ◽  
Vol 15 ◽  
pp. 57-62
Author(s):  
Karel Mikeš ◽  
Ondřej Rokoš ◽  
Ron H. J. Peerlings
Keyword(s):  
Adaptive Mesh Refinement ◽  
Deformation Gradient ◽  
Hexagonal Lattice ◽  
Computational Cost ◽  
Adaptive Mesh ◽  
Nanoindentation Test ◽  
Atomistic Model ◽  
Molecular Statics ◽  
Quasicontinuum Method ◽  
Local Lattice

In this work, molecular statics is used to model a nanoindentation test on a two-dimensional hexagonal lattice. To this end, the QuasiContinuum (QC) method with adaptive propagation of the fully resolved domain is used to reduce the computational cost required by the full atomistic model. Three different adaptive mesh refinement criteria are introduced and tested, based on: (i) the Zienkiewicz–Zhu criterion (used for the deformation gradient), (ii) local atoms’ site energy, and (iii) local lattice disregistry. Accuracy and efficiency of individual refinement schemes are compared against the full atomistic model and obtained results are discussed.

scholarly journals Implementation and performance of adaptive mesh refinement in the Ice Sheet System Model (ISSM v4.14)

2019 ◽  
Vol 12 (1) ◽  
pp. 215-232 ◽  
Author(s):  
Thiago Dias dos Santos ◽  
Mathieu Morlighem ◽  
Hélène Seroussi ◽  
Philippe Remy Bernard Devloo ◽  
Jefferson Cardia Simões
Keyword(s):  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Computational Cost ◽  
Ice Sheet ◽  
Adaptive Mesh ◽  
System Model ◽  
Computational Time ◽  
Error Estimator ◽  
Fine Mesh ◽  
Grounding Line

Abstract. Accurate projections of the evolution of ice sheets in a changing climate require a fine mesh/grid resolution in ice sheet models to correctly capture fundamental physical processes, such as the evolution of the grounding line, the region where grounded ice starts to float. The evolution of the grounding line indeed plays a major role in ice sheet dynamics, as it is a fundamental control on marine ice sheet stability. Numerical modeling of a grounding line requires significant computational resources since the accuracy of its position depends on grid or mesh resolution. A technique that improves accuracy with reduced computational cost is the adaptive mesh refinement (AMR) approach. We present here the implementation of the AMR technique in the finite element Ice Sheet System Model (ISSM) to simulate grounding line dynamics under two different benchmarks: MISMIP3d and MISMIP+. We test different refinement criteria: (a) distance around the grounding line, (b) a posteriori error estimator, the Zienkiewicz–Zhu (ZZ) error estimator, and (c) different combinations of (a) and (b). In both benchmarks, the ZZ error estimator presents high values around the grounding line. In the MISMIP+ setup, this estimator also presents high values in the grounded part of the ice sheet, following the complex shape of the bedrock geometry. The ZZ estimator helps guide the refinement procedure such that AMR performance is improved. Our results show that computational time with AMR depends on the required accuracy, but in all cases, it is significantly shorter than for uniformly refined meshes. We conclude that AMR without an associated error estimator should be avoided, especially for real glaciers that have a complex bed geometry.

scholarly journals Hydrodynamical Adaptive Mesh Refinement Simulations of Disk Galaxies

2008 ◽  
Vol 4 (S254) ◽  
pp. 445-452
Author(s):  
Brad K. Gibson ◽  
Stéphanie Courty ◽  
Patricia Sánchez-Blázquez ◽  
Romain Teyssier ◽  
Elisa L. House ◽  
...  
Keyword(s):  
Galaxy Formation ◽  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Disk Galaxies ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Temporal And Spatial ◽  
Compare And Contrast

AbstractTo date, fully cosmological hydrodynamic disk simulations to redshift zero have only been undertaken with particle-based codes, such as GADGET, Gasoline, or GCD+. In light of the (supposed) limitations of traditional implementations of smoothed particle hydrodynamics (SPH), or at the very least, their respective idiosyncrasies, it is important to explore complementary approaches to the SPH paradigm to galaxy formation. We present the first high-resolution cosmological disk simulations to redshift zero using an adaptive mesh refinement (AMR)-based hydrodynamical code, in this case, RAMSES. We analyse the temporal and spatial evolution of the simulated stellar disks' vertical heating, velocity ellipsoids, stellar populations, vertical and radial abundance gradients (gas and stars), assembly/infall histories, warps/lopsideness, disk edges/truncations (gas and stars), ISM physics implementations, and compare and contrast these properties with our sample of cosmological SPH disks, generated with GCD+. These preliminary results are the first in our long-term Galactic Archaeology Simulation program.

scholarly journals Implementing and comparing sink particles in AMR and SPH

2010 ◽  
Vol 6 (S270) ◽  
pp. 425-428 ◽  
Author(s):  
Christoph Federrath ◽  
Robi Banerjee ◽  
Daniel Seifried ◽  
Paul C. Clark ◽  
Ralf S. Klessen
Keyword(s):  
Star Formation ◽  
Adaptive Mesh Refinement ◽  
Star Formation Rate ◽  
Formation Rate ◽  
Particle Creation ◽  
Adaptive Mesh ◽  
Particle Properties ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Density Threshold

AbstractWe implemented sink particles in the Adaptive Mesh Refinement (AMR) code FLASH to model the gravitational collapse and accretion in turbulent molecular clouds and cores. Sink particles are frequently used to measure properties of star formation in numerical simulations, such as the star formation rate and efficiency, and the mass distribution of stars. We show that only using a density threshold for sink particle creation is insufficient in case of supersonic flows, because the density can exceed the threshold in strong shocks that do not necessarily lead to local collapse. Additional physical collapse indicators have to be considered. We apply our AMR sink particle module to the formation of a star cluster, and compare it to a Smoothed Particle Hydrodynamics (SPH) code with sink particles. Our comparison shows encouraging agreement of gas and sink particle properties between the AMR and SPH code.

scholarly journals Numerical Hydrodynamics: SPH versus AMR

2001 ◽  
Vol 200 ◽  
pp. 563-566
Author(s):  
Tomek Plewa
Keyword(s):  
Smoothed Particle Hydrodynamics ◽  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Computational Hydrodynamics ◽  
Advantages And Disadvantages ◽  
Numerical Hydrodynamics ◽  
Particle Hydrodynamics ◽  
Smoothed Particle

The advantages and disadvantages of two approaches to astrophysical hydrodynamics, Smoothed Particle Hydrodynamics (SPH) and Adaptive Mesh Refinement (AMR), are briefly discussed together with some current problems of computational hydrodynamics.

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