Multiscale high-order/low-order (HOLO) algorithms and applications

Chacon, Luis; Chen, Guangye; Knoll, Dana Alan; Newman, Christopher Kyle; Park, HyeongKae; Taitano, William; Willert, Jeff A.; Womeldorff, Geoffrey Alan

doi:10.1016/j.jcp.2016.10.069

Title: Multiscale high-order/low-order (HOLO) algorithms and applications

Abstract

Here, we review the state of the art in the formulation, implementation, and performance of so-called high-order/low-order (HOLO) algorithms for challenging multiscale problems. HOLO algorithms attempt to couple one or several high-complexity physical models (the high-order model, HO) with low-complexity ones (the low-order model, LO). The primary goal of HOLO algorithms is to achieve nonlinear convergence between HO and LO components while minimizing memory footprint and managing the computational complexity in a practical manner. Key to the HOLO approach is the use of the LO representations to address temporal stiffness, effectively accelerating the convergence of the HO/LO coupled system. The HOLO approach is broadly underpinned by the concept of nonlinear elimination, which enables segregation of the HO and LO components in ways that can effectively use heterogeneous architectures. The accuracy and efficiency benefits of HOLO algorithms are demonstrated with specific applications to radiation transport, gas dynamics, plasmas (both Eulerian and Lagrangian formulations), and ocean modeling. Across this broad application spectrum, HOLO algorithms achieve significant accuracy improvements at a fraction of the cost compared to conventional approaches. It follows that HOLO algorithms hold significant potential for high-fidelity system scale multiscale simulations leveraging exascale computing.

Authors:

^[1];

^[1]; Knoll, Dana Alan ^[1]; Newman, Christopher Kyle ^[1];

^[1];

^[1]; Willert, Jeff A. ^[2];

^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Institute for Defense Analyses, Alexandria, VA (United States)

Publication Date:: Fri Nov 11 00:00:00 EST 2016

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1375167

Alternate Identifier(s):: OSTI ID: 1397820

Report Number(s):: LA-UR-16-23721
Journal ID: ISSN 0021-9991

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Computational Physics

Additional Journal Information:: Journal Volume: 330; Journal Issue: C; Journal ID: ISSN 0021-9991

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; Mathematics; High-order/low-order; HOLO; Multiscale algorithms; Implicit timestepping; Communication avoiding algorithms

Citation Formats


                    Chacon, Luis, Chen, Guangye, Knoll, Dana Alan, Newman, Christopher Kyle, Park, HyeongKae, Taitano, William, Willert, Jeff A., and Womeldorff, Geoffrey Alan. Multiscale high-order/low-order (HOLO) algorithms and applications.  United States: N. p., 2016. 
Web.  doi:10.1016/j.jcp.2016.10.069.

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                    Chacon, Luis, Chen, Guangye, Knoll, Dana Alan, Newman, Christopher Kyle, Park, HyeongKae, Taitano, William, Willert, Jeff A., & Womeldorff, Geoffrey Alan. Multiscale high-order/low-order (HOLO) algorithms and applications.  United States.  https://doi.org/10.1016/j.jcp.2016.10.069

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                    Chacon, Luis, Chen, Guangye, Knoll, Dana Alan, Newman, Christopher Kyle, Park, HyeongKae, Taitano, William, Willert, Jeff A., and Womeldorff, Geoffrey Alan. Fri .  
"Multiscale high-order/low-order (HOLO) algorithms and applications".  United States.  https://doi.org/10.1016/j.jcp.2016.10.069.  https://www.osti.gov/servlets/purl/1375167.

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@article{osti_1375167,

  title        = {Multiscale high-order/low-order (HOLO) algorithms and applications},

  author       = {Chacon, Luis and Chen, Guangye and Knoll, Dana Alan and Newman, Christopher Kyle and Park, HyeongKae and Taitano, William and Willert, Jeff A. and Womeldorff, Geoffrey Alan},

  abstractNote = {Here, we review the state of the art in the formulation, implementation, and performance of so-called high-order/low-order (HOLO) algorithms for challenging multiscale problems. HOLO algorithms attempt to couple one or several high-complexity physical models (the high-order model, HO) with low-complexity ones (the low-order model, LO). The primary goal of HOLO algorithms is to achieve nonlinear convergence between HO and LO components while minimizing memory footprint and managing the computational complexity in a practical manner. Key to the HOLO approach is the use of the LO representations to address temporal stiffness, effectively accelerating the convergence of the HO/LO coupled system. The HOLO approach is broadly underpinned by the concept of nonlinear elimination, which enables segregation of the HO and LO components in ways that can effectively use heterogeneous architectures. The accuracy and efficiency benefits of HOLO algorithms are demonstrated with specific applications to radiation transport, gas dynamics, plasmas (both Eulerian and Lagrangian formulations), and ocean modeling. Across this broad application spectrum, HOLO algorithms achieve significant accuracy improvements at a fraction of the cost compared to conventional approaches. It follows that HOLO algorithms hold significant potential for high-fidelity system scale multiscale simulations leveraging exascale computing.},

  doi          = {10.1016/j.jcp.2016.10.069},

  journal      = {Journal of Computational Physics},

  number       = C,

  volume       = 330,

  place        = {United States},

  year         = {Fri Nov 11 00:00:00 EST 2016},

  month        = {Fri Nov 11 00:00:00 EST 2016}

}

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Works referencing / citing this record:

Advances and challenges in computational fluid dynamics of atmospheric pressure plasmas
journal, September 2018

Trelles, Juan Pablo
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Title: Multiscale high-order/low-order (HOLO) algorithms and applications

Abstract

Citation Formats

A quasi-diffusion method of solving the kinetic equation journal, January 1964

Diffusion Synthetic Acceleration Methods for the Diamond-Differenced Discrete-Ordinates Equations journal, October 1977

A grey transport acceleration method far time-dependent radiative transfer problems journal, October 1988

Implicit moment particle simulation of plasmas journal, June 1981

Time-filtering particle simulations with ωpe Δt ⪢ 1 journal, August 1981

An implicit method for electromagnetic plasma simulation in two dimensions journal, May 1982

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An Analysis of Approximate Nonlinear Elimination journal, March 1996

CELEST1D: an implicit, fully kinetic model for low-frequency, electromagnetic plasma simulation journal, March 1992

Development of a Consistent and Stable Fully Implicit Moment Method for Vlasov--Ampère Particle in Cell (PIC) System journal, January 2013

Application of the Jacobian-Free Newton-Krylov Method to Nonlinear Acceleration of Transport Source Iteration in Slab Geometry journal, February 2011

Nonlinear Acceleration of Transport Criticality Problems journal, September 2012

A Consistent, Moment-Based, Multiscale Solution Approach for Thermal Radiative Transfer Problems journal, May 2012

Moment-Based Acceleration for Neutral Gas Kinetics with BGK Collision Operator journal, July 2014

Fluid preconditioning for Newton–Krylov-based, fully implicit, electrostatic particle-in-cell simulations journal, February 2014

An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D-3V Vlasov–Darwin particle-in-cell algorithm journal, October 2014

A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov–Darwin particle-in-cell algorithm journal, December 2015

Hybrid Krylov Methods for Nonlinear Systems of Equations journal, May 1990

Jacobian-free Newton–Krylov methods: a survey of approaches and applications journal, January 2004

Iterative Procedures for Nonlinear Integral Equations journal, October 1965

Anderson Acceleration for Fixed-Point Iterations journal, January 2011

An Efficient and Time Accurate, Moment-Based Scale-Bridging Algorithm for Thermal Radiative Transfer Problems journal, January 2013

Residual Monte Carlo high-order solver for Moment-Based Accelerated Thermal Radiative Transfer equations journal, November 2014

A comparison of acceleration methods for solving the neutron transport k -eigenvalue problem journal, October 2014

Moment-Based Acceleration of Monte Carlo Solution for Multifrequency Thermal Radiative Transfer Problems journal, October 2014

Monte Carlo simulation methods in moment-based scale-bridging algorithms for thermal radiative-transfer problems journal, March 2015

Applying Nonlinear Diffusion Acceleration to the Neutron Transport k -Eigenvalue Problem with Anisotropic Scattering journal, November 2015

Simulation of Radiation Transport in a Channel Based on the Quasi-Diffusion Method journal, December 2008

Consistent Spatial Approximation of the Low-Order Quasi-Diffusion Equations on Coarse Grids journal, February 2005

A Functional Monte Carlo Method for k -Eigenvalue Problems journal, June 2008

Multilevel Quasidiffusion Methods for Solving Multigroup Neutron Transport k -Eigenvalue Problems in One-Dimensional Slab Geometry journal, October 2011

A cell-local finite difference discretization of the low-order quasidiffusion equations for neutral particle transport on unstructured quadrilateral meshes journal, September 2014

Convergence Analysis of the Nonlinear Coarse-Mesh Finite Difference Method for One-Dimensional Fixed-Source Neutron Diffusion Problem journal, June 2004

Unstructured partial- and net-current based coarse mesh finite difference acceleration applied to the extended step characteristics method in NEWT journal, February 2011

Hybrid Monte Carlo-CMFD Methods for Accelerating Fission Source Convergence journal, July 2013

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Whole-Core Transport Solutions with 2-D/1-D Fusion Kernel via p-CMFD Acceleration and p-CMFD Embedding of Nonoverlapping Local/Global Iterations journal, September 2015

A synthetically accelerated scheme for radiative transfer calculations journal, May 1993

A Linear-Discontinuous Spatial Differencing Scheme forSnRadiative Transfer Calculations journal, October 1996

A Transport Synthetic Acceleration Method for Transport Iterations journal, March 1997

Fast iterative methods for discrete-ordinates particle transport calculations journal, January 2002

Krylov Iterative Methods and the Degraded Effectiveness of Diffusion Synthetic Acceleration for Multidimensional S N Calculations in Problems with Material Discontinuities journal, July 2004

A Hybrid Deterministic/Monte Carlo Method for Solving the k -Eigenvalue Problem with a Comparison to Analog Monte Carlo Solutions journal, August 2014

An implicit Monte Carlo scheme for calculating time and frequency dependent nonlinear radiation transport journal, December 1971

Implicit Monte Carlo Diffusion—An Acceleration Method for Monte Carlo Time-Dependent Radiative Transfer Simulations journal, September 2001

A hybrid transport-diffusion method for Monte Carlo radiative-transfer simulations journal, March 2007

A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws journal, April 1978

An energy- and charge-conserving, implicit, electrostatic particle-in-cell algorithm journal, August 2011

Implicit time integration for plasma simulation journal, August 1982

Direct implicit large time-step particle simulation of plasmas journal, July 1983

Implicit particle simulation of magnetized plasmas journal, December 1983

An electromagnetic field algorithm for 2D implicit plasma simulation journal, August 1987

Electromagnetic direct implicit plasma simulation journal, September 1987

A second-order implicit particle mover with adjustable damping journal, October 1990

Implicit particle simulation of electromagnetic plasma phenomena journal, May 1992

The Darwin Direct Implicit Particle-in-Cell (DADIPIC) Method for Simulation of Low Frequency Plasma Phenomena journal, September 1995

Performance and optimization of direct implicit particle simulation journal, March 1989

The energy conserving particle-in-cell method journal, August 2011

Particle acceleration and energy conservation in particle in cell simulations journal, July 2011

Elimination of electromagnetic radiation in plasma simulation: The Darwin or magneto inductive approximation journal, October 1985

An analysis of the Darwin model of approximation to Maxwell’s equations journal, January 1992

A hierarchy of approximate models for the Maxwell equations journal, May 1996

A unified approach to the Darwin approximation journal, October 2007

An analytical particle mover for the charge- and energy-conserving, nonlinearly implicit, electrostatic particle-in-cell algorithm journal, August 2013

A charge- and energy-conserving implicit, electrostatic particle-in-cell algorithm on mapped computational meshes journal, January 2013

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Implicit and Conservative Difference Scheme for the Fokker-Planck Equation journal, June 1994

An Implicit Energy-Conservative 2D Fokker–Planck Algorithm journal, January 2000

An Implicit Energy-Conservative 2D Fokker–Planck Algorithm journal, January 2000

Fully Implicit Kinetic Solution of Collisional Plasmas journal, September 1997

A quasi-diffusion method of solving the kinetic equation
journal, January 1964

Diffusion Synthetic Acceleration Methods for the Diamond-Differenced Discrete-Ordinates Equations
journal, October 1977

A grey transport acceleration method far time-dependent radiative transfer problems
journal, October 1988

Implicit moment particle simulation of plasmas
journal, June 1981

Time-filtering particle simulations with ωpe Δt ⪢ 1
journal, August 1981

An implicit method for electromagnetic plasma simulation in two dimensions
journal, May 1982

Implicit free-surface method for the Bryan-Cox-Semtner ocean model
journal, January 1994

An Analysis of Approximate Nonlinear Elimination
journal, March 1996

CELEST1D: an implicit, fully kinetic model for low-frequency, electromagnetic plasma simulation
journal, March 1992

Development of a Consistent and Stable Fully Implicit Moment Method for Vlasov--Ampère Particle in Cell (PIC) System
journal, January 2013

Application of the Jacobian-Free Newton-Krylov Method to Nonlinear Acceleration of Transport Source Iteration in Slab Geometry
journal, February 2011

Nonlinear Acceleration of Transport Criticality Problems
journal, September 2012

A Consistent, Moment-Based, Multiscale Solution Approach for Thermal Radiative Transfer Problems
journal, May 2012

Moment-Based Acceleration for Neutral Gas Kinetics with BGK Collision Operator
journal, July 2014

Fluid preconditioning for Newton–Krylov-based, fully implicit, electrostatic particle-in-cell simulations
journal, February 2014

An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D-3V Vlasov–Darwin particle-in-cell algorithm
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Hybrid Krylov Methods for Nonlinear Systems of Equations
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Jacobian-free Newton–Krylov methods: a survey of approaches and applications
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Iterative Procedures for Nonlinear Integral Equations
journal, October 1965

Anderson Acceleration for Fixed-Point Iterations
journal, January 2011

An Efficient and Time Accurate, Moment-Based Scale-Bridging Algorithm for Thermal Radiative Transfer Problems
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A Functional Monte Carlo Method for k -Eigenvalue Problems
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Multilevel Quasidiffusion Methods for Solving Multigroup Neutron Transport k -Eigenvalue Problems in One-Dimensional Slab Geometry
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A cell-local finite difference discretization of the low-order quasidiffusion equations for neutral particle transport on unstructured quadrilateral meshes
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Convergence Analysis of the Nonlinear Coarse-Mesh Finite Difference Method for One-Dimensional Fixed-Source Neutron Diffusion Problem
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Unstructured partial- and net-current based coarse mesh finite difference acceleration applied to the extended step characteristics method in NEWT
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Hybrid Monte Carlo-CMFD Methods for Accelerating Fission Source Convergence
journal, July 2013

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journal, September 2014

Whole-Core Transport Solutions with 2-D/1-D Fusion Kernel via p-CMFD Acceleration and p-CMFD Embedding of Nonoverlapping Local/Global Iterations
journal, September 2015

A synthetically accelerated scheme for radiative transfer calculations
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A Linear-Discontinuous Spatial Differencing Scheme forSnRadiative Transfer Calculations
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Krylov Iterative Methods and the Degraded Effectiveness of Diffusion Synthetic Acceleration for Multidimensional S _N Calculations in Problems with Material Discontinuities
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A Hybrid Deterministic/Monte Carlo Method for Solving the k -Eigenvalue Problem with a Comparison to Analog Monte Carlo Solutions
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Implicit Monte Carlo Diffusion—An Acceleration Method for Monte Carlo Time-Dependent Radiative Transfer Simulations
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A hybrid transport-diffusion method for Monte Carlo radiative-transfer simulations
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A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
journal, April 1978

An energy- and charge-conserving, implicit, electrostatic particle-in-cell algorithm
journal, August 2011

Implicit time integration for plasma simulation
journal, August 1982

Direct implicit large time-step particle simulation of plasmas
journal, July 1983

Implicit particle simulation of magnetized plasmas
journal, December 1983

An electromagnetic field algorithm for 2D implicit plasma simulation
journal, August 1987

Electromagnetic direct implicit plasma simulation
journal, September 1987

A second-order implicit particle mover with adjustable damping
journal, October 1990

Implicit particle simulation of electromagnetic plasma phenomena
journal, May 1992

The Darwin Direct Implicit Particle-in-Cell (DADIPIC) Method for Simulation of Low Frequency Plasma Phenomena
journal, September 1995

Performance and optimization of direct implicit particle simulation
journal, March 1989

The energy conserving particle-in-cell method
journal, August 2011

Particle acceleration and energy conservation in particle in cell simulations
journal, July 2011

Elimination of electromagnetic radiation in plasma simulation: The Darwin or magneto inductive approximation
journal, October 1985

An analysis of the Darwin model of approximation to Maxwell’s equations
journal, January 1992

A hierarchy of approximate models for the Maxwell equations
journal, May 1996

A unified approach to the Darwin approximation
journal, October 2007

An analytical particle mover for the charge- and energy-conserving, nonlinearly implicit, electrostatic particle-in-cell algorithm
journal, August 2013

A charge- and energy-conserving implicit, electrostatic particle-in-cell algorithm on mapped computational meshes
journal, January 2013

A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions
journal, July 2016

Analysis of the time integration in plasma simulation
journal, February 1979

Nonlocal Magnetic-Field Generation in Plasmas without Density Gradients
journal, January 2002

An implicit Vlasov–Fokker–Planck code to model non-local electron transport in 2-D with magnetic fields
journal, February 2004

Magnetic Cavitation and the Reemergence of Nonlocal Transport in Laser Plasmas
journal, February 2008

Nonlinear Kinetic Transport of Electrons and Magnetic Field in Laser-Produced Plasmas
journal, August 1985

Magnetic Field and Nonlocal Transport in Laser-Created Plasmas
journal, November 1985

A code for the solution of the Vlasov-Fokker-Planck equation in 1-D or 2-D
journal, December 1988

Implicit and Conservative Difference Scheme for the Fokker-Planck Equation
journal, June 1994

An Implicit Energy-Conservative 2D Fokker–Planck Algorithm
journal, January 2000

An Implicit Energy-Conservative 2D Fokker–Planck Algorithm
journal, January 2000

Fully Implicit Kinetic Solution of Collisional Plasmas
journal, September 1997

Collisional Effects in Plasmas Modelled by a Simplified Fokker-Planck Equation
journal, July 1993

Rapid self-magnetization of laser speckles in plasmas by nonlinear anisotropic instability
journal, March 2009

A review of Vlasov–Fokker–Planck numerical modeling of inertial confinement fusion plasma
journal, February 2012