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 Accelerating numerical wave propagation by wavefield adapted meshes. Part II: full-waveform inversion

2020 ◽  
Vol 221 (3) ◽  
pp. 1591-1604 ◽  
Author(s):  
Solvi Thrastarson ◽  
Martin van Driel ◽  
Lion Krischer ◽  
Christian Boehm ◽  
Michael Afanasiev ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Spectral Element ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Order Of Magnitude ◽  
Numerical Wave ◽  
Expected Complexity

SUMMARY We present a novel full-waveform inversion (FWI) approach which can reduce the computational cost by up to an order of magnitude compared to conventional approaches, provided that variations in medium properties are sufficiently smooth. Our method is based on the usage of wavefield adapted meshes which accelerate the forward and adjoint wavefield simulations. By adapting the mesh to the expected complexity and smoothness of the wavefield, the number of elements needed to discretize the wave equation can be greatly reduced. This leads to spectral-element meshes which are optimally tailored to source locations and medium complexity. We demonstrate a workflow which opens up the possibility to use these meshes in FWI and show the computational advantages of the approach. We provide examples in 2-D and 3-D to illustrate the concept, describe how the new workflow deviates from the standard FWI workflow, and explain the additional steps in detail.

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 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.

A 3D Complexity-Adaptive Approach to Exploit Sparsity in Elastic Wave Propagation

Geophysics ◽  
2021 ◽  
pp. 1-64
Author(s):  
Claudia Haindl ◽  
Kuangdai Leng ◽  
Tarje Nissen-Meyer
Keyword(s):  
Degrees Of Freedom ◽  
Computational Cost ◽  
Parameter Tuning ◽  
Performance Limits ◽  
Absorbing Boundary ◽  
Adaptive Approach ◽  
Order Of Magnitude ◽  
Speed Up ◽  
Complex Settings ◽  
Close Fit

We present an adaptive approach to seismic modeling by which the computational cost of a 3D simulation can be reduced while retaining resolution and accuracy. This Azimuthal Complexity Adaptation (ACA) approach relies upon the inherent smoothness of wavefields around the azimuth of a source-centered cylindrical coordinate system. Azimuthal oversampling is thereby detected and eliminated. The ACA method has recently been introduced as part of AxiSEM3D, an open-source solver for global seismology. We employ a generalization of this solver which can handle local-scale Cartesian models, and which features a combination of an absorbing boundary condition and a sponge boundary with automated parameter tuning. The ACA method is benchmarked against an established 3D method using a model featuring bathymetry and a salt body. We obtain a close fit where the models are implemented equally in both solvers and an expectedly poor fit otherwise, with the ACA method running an order of magnitude faster than the classic 3D method. Further, we present maps of maximum azimuthal wavenumbers that are created to facilitate azimuthal complexity adaptation. We show how these maps can be interpreted in terms of the 3D complexity of the wavefield and in terms of seismic resolution. The expected performance limits of the ACA method for complex 3D structures are tested on the SEG/EAGE salt model. In this case, ACA still reduces the overall degrees of freedom by 92% compared to a complexity-blind AxiSEM3D simulation. In comparison with the reference 3D method, we again find a close fit and a speed-up of a factor 7. We explore how the performance of ACA is affected by model smoothness by subjecting the SEG/EAGE salt model to Gaussian smoothing. This results in a doubling of the speed-up. ACA thus represents a convergent, versatile and efficient method for a variety of complex settings and scales.

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.

Multidimensional Modeling and Validation of Dual-Fuel Combustion in a Large Bore Medium Speed Diesel Engine

2015 ◽  
Author(s):  
Sameera Wijeyakulasuriya ◽  
Ravichandra S. Jupudi ◽  
Shawn Givler ◽  
Roy J. Primus ◽  
Adam E. Klingbeil ◽  
...  
Keyword(s):  
Diesel Engine ◽  
Natural Gas ◽  
Adaptive Mesh Refinement ◽  
Computational Cost ◽  
Adaptive Mesh ◽  
Cylinder Wall ◽  
Detailed Chemical Kinetics ◽  
Substitution Rates ◽  
Numerical Predictions ◽  
Medium Speed

High fidelity, three-dimensional CFD was used to model the flow, fuel injection, combustion, and emissions in a large bore medium speed diesel engine with different levels of natural gas substitution. Detailed chemical kinetics was used to model the complex combustion behavior of the premixed natural gas, ignited via a diesel spray. The numerical predictions were compared against measured multiple cycle pressure data, to understand the possible factors affecting cyclic variation in experimental data. Under conditions with high natural gas substitution rates, diesel was injected much earlier than firing-TDC. This additional mixing time allowed the active radicals from diesel dissociation to initiate combustion from the cylinder wall and propagate inwards. 0%, 60%, and 93% natural gas substitution rates (by energy) were tested in this study to develop computational capabilities needed to accurately model and understand the underlying physics. Several innovative computational methods such as adaptive mesh refinement (which automatically refines and coarsens the mesh based on the existing solution parameters), and multi-zoning (which groups chemically similar cells together to reduce combustion calculation time) were utilized to obtain accurate predictions at a lower computational cost. Important engine emissions such as NOx, CO, unburnt HC, and soot were predicted numerically and compared against measured engine data.

Improved Mappings for Streamline-Based Simulation

SPE Journal ◽  
2006 ◽  
Vol 11 (03) ◽  
pp. 294-302 ◽  
Author(s):  
Bradley T. Mallison ◽  
Margot G. Gerritsen ◽  
Sebastien F. Matringe
Keyword(s):  
Mass Balance ◽  
Adaptive Mesh Refinement ◽  
Piecewise Linear ◽  
Gas Injection ◽  
Computational Cost ◽  
Adaptive Mesh ◽  
Linear Representation ◽  
Compositional Simulation ◽  
Background Grid ◽  
Streamline Method

Summary Our interest lies in extending the streamline method to compositional simulation. In this paper, we develop improved mappings to and from streamlines that are necessary to obtain reliable predictions of gas injection processes. Our improved mapping to streamlines uses a piecewise linear representation of saturations on the background grid in order to minimize numerical smearing. Our strategy for mapping saturations from streamlines to the background grid is based on kriging. We test our improvements to the streamline method by use of a simple model for miscible flooding based on incompressible Darcy flow. Results indicate that our mappings offer improved resolution and reduce mass-balance errors relative to the commonly used mappings. Our mappings also require fewer streamlines to achieve a desired level of accuracy. In compositional cases where the computational cost of a streamline solve is high, we anticipate that this will lead to an improvement in the efficiency of streamline-based simulation. Introduction The overall goal of our research is to improve the accuracy and efficiency of the streamline method in simulating compositional problems such as those that occur in miscible or near-miscible gas injection processes. This is our second paper suggesting improvements to this end. In Mallison et al. (2005) we investigated a 1D compositional finite-difference solver based on a high-order upwind scheme and adaptive mesh refinement that is appropriate for use in a compositional streamline simulator. Here, we propose new mappings to and from streamlines that improve the accuracy of the streamline method for problems in which the flow pattern does not remain fixed for large time intervals. Such problems require that streamlines be periodically updated in order to account for changing flow directions and for the treatment of gravity terms (Thiele et al. 1996; Bratvedt et al. 1996). For each set of streamlines, fluids must be mapped from an underlying background grid, on which the pressure is solved (or, say, the flow), to the streamlines, moved forward in time, and then mapped from the streamlines back to the background grid. The mappings introduce numerical smearing and generally also mass-balance errors. When streamlines are updated frequently, the mapping errors limit the overall accuracy of the streamline method. Our improved mapping algorithms are aimed at minimizing this type of error.

scholarly journals Implementation and Performance of Adaptive Mesh Refinement in the Ice Sheet System Model (ISSM v4.14)

2018 ◽  
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 ◽  
Grounding Line ◽  
Refined Meshes

Abstract. Accurate projections of the evolution of ice sheets in a changing climate require a fine mesh/grid resolution 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 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 approach, AMR. 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 grounding line, (b) a posteriori error estimator, the Zienkiewicz-Zhu (ZZ) error estimator, and (c) different combinations of (a) and (b). We find that for MISMIP3d setup, refining 5 km around the grounding line, both on grounded and floating ice, is sufficient to produce AMR results similar to the ones obtained with uniformly refined meshes. However, for the MISMIP+ setup, we note that there is a minimum distance of 30 km around the grounding line required to produce accurate results. We find this AMR mesh-dependency is linked to the complex bedrock topography of MISMIP+. In both benchmarks, the ZZ error estimator presents high values around the grounding line. Particularly for MISMIP+ setup, the estimator also presents high values in the grounded part of the ice sheet, following the complex shape of the bedrock geometry. This 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 Efficient Simulations of Propagating Flames and Fire Suppression Optimization Using Adaptive Mesh Refinement

Fluids ◽  
2021 ◽  
Vol 6 (9) ◽  
pp. 323
Author(s):  
Caelan Lapointe ◽  
Nicholas T. Wimer ◽  
Sam Simons-Wellin ◽  
Jeffrey F. Glusman ◽  
Gregory B. Rieker ◽  
...  
Keyword(s):  
Adaptive Mesh Refinement ◽  
Optimization Problems ◽  
Solid Phase ◽  
Fire Suppression ◽  
Spatial Scales ◽  
Mesh Refinement ◽  
Computational Cost ◽  
Adaptive Mesh ◽  
Fire Spread ◽  
Wide Range

Fires are complex multi-physics problems that span wide spatial scale ranges. Capturing this complexity in computationally affordable numerical simulations for process studies and “outer-loop” techniques (e.g., optimization and uncertainty quantification) is a fundamental challenge in reacting flow research. Further complications arise for propagating fires where a priori knowledge of the fire spread rate and direction is typically not available. In such cases, static mesh refinement at all possible fire locations is a computationally inefficient approach to bridging the wide range of spatial scales relevant to fire behavior. In the present study, we address this challenge by incorporating adaptive mesh refinement (AMR) in fireFoam, an OpenFOAM solver for simulations of complex fire phenomena involving pyrolyzing solid surfaces. The AMR functionality in the extended solver, called fireDyMFoam, is load balanced, models gas, solid, and liquid phases, and allows us to dynamically track regions of interest, thus avoiding inefficient over-resolution of areas far from a propagating flame. We demonstrate the AMR capability and computational efficiency for fire spread on vertical panels, showing that the AMR solver reproduces results obtained using much larger statically refined meshes, but at a substantially reduced computational cost. We then leverage AMR in an optimization framework for fire suppression based on the open-source Dakota toolkit, which is made more computationally tractable through the use of fireDyMFoam, minimizing a cost function that balances water use and solid-phase mass loss. The extension of fireFoam developed here thus enables the use of higher fidelity simulations in optimization problems for the suppression of fire spread in both built and natural environments.

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