A Scalable Semi‐Implicit Barotropic Mode Solver for the MPAS‐Ocean

Kang, Hyun-Gyu; Evans, Katherine J.; Petersen, Mark; Jones, Philip W.; Bishnu, Siddhartha

doi:10.1029/2020ms002238

Cited by 5 publications

(13 citation statements)

References 64 publications

(148 reference statements)

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“…The procedure for obtaining the semi-implicit barotropic thickness equation in MPAS-O is described in detail in Kang et al (2021); the resulting elliptic equation is written as…”

Section: The Barotropic System In Mpas-omentioning

confidence: 99%

“…More detailed procedures will be described later in this section. An implicitness parameter α is set as 0.5 to use the Crank-Nicolson method as in Kang et al (2021). The coefficient matrix constructed for the left hand side of equations ( 3) and ( 4) is not symmetric due to the different areas of each cell in the divergence operator.…”

Section: The Barotropic System In Mpas-omentioning

confidence: 99%

“…The coefficient matrix constructed for the left hand side of equations ( 3) and ( 4) is not symmetric due to the different areas of each cell in the divergence operator. By multiplying or scaling equations ( 3) and (4) via the area of each cell q, the coefficient matrix becomes symmetric and positive definite (see Appendix in Kang et al (2021)). This is a useful transformation since there are many efficient iterative solvers and preconditioners for symmetric systems.…”

Section: The Barotropic System In Mpas-omentioning

confidence: 99%

“…To obtain ζ l , an outer iteration is performed using ζ n in the divergence operator (BAROTROPIC THICKNESS (OUTER) in Figure 1). Once ζ l is known, the barotropic velocity is updated using the equation (9b) in Kang et al (2021). With two lagged values, the right hand side of equation ( 3) is recomputed.…”

Section: The Barotropic System In Mpas-omentioning

confidence: 99%

“…The Fortran hand-crafted (FHC) solver. As a reference of performance benchmarks throughout later sections, we use the FHC solver currently implemented in MPAS-O (Kang et al 2021). The FHC solver introduces the PBiCGStab algorithm (Cools and Vanroose 2017), where two global synchronization points per iteration (line 10 and 19 in Algorithm 1) that can be overlapped with the preconditioning and matrix-vector multiplication processes (illustrated between the "Begin reduction" and "End reduction" statements).…”

Section: Linear Iterative Solversmentioning

confidence: 99%

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An implicit barotropic mode solver for MPAS-ocean using a modern Fortran solver interface

Kang,

Tuminaro,

Prokopenko

et al. 2023

The International Journal of High Performance Computing Applica

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We demonstrate use of a modern Fortran solver interface to manage solver algorithms for an implicit barotropic mode solver in the Model for Predictions Across Scales-Ocean (MPAS-O). ForTrilinos, a Fortran interface to Trilinos that contains a large collection of solver capabilities written in C++, has been implemented in MPAS-O to provide access to a suite of linear solver options. By virtue of the simplified wrapper and interface generator (SWIG) automation tool that generates modern Fortran interfaces to C++ code, we were able to implement the Fortran solver interface in MPAS-O using a familiar Fortran coding style while minimizing performance degradation. The ForTrilinos solver interface is written within MPAS-O’s time stepping modules as a subroutine in conjunction with MPAS-O code. Applied to an idealized ocean and a high-resolution realistic ocean test case, parallel performance of ForTrilinos solvers is examined. It is found that parallel scalability of the ForTrilinos solvers is highly dependent on the number of global synchronization points per solver iteration in each iterative solver algorithm. ForTrilinos solvers perform best compared to the Fortran hand-crafted (FHC) solver when the amount of work per processor is large enough. However, parallel scalability is better with the FHC solver and so when the work per core is modest FHC outperforms ForTrilinos. The intercomparison between the ForTrilinos and FHC solvers reveals that this performance hit in the ForTrilinos solver mostly comes from the global synchronization process, while suggesting that the matrix-vector multiplication process in the FHC solver needs to be optimized for better performance.

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“…The procedure for obtaining the semi-implicit barotropic thickness equation in MPAS-O is described in detail in Kang et al (2021); the resulting elliptic equation is written as…”

Section: The Barotropic System In Mpas-omentioning

confidence: 99%

Section: The Barotropic System In Mpas-omentioning

confidence: 99%

Section: The Barotropic System In Mpas-omentioning

confidence: 99%

Section: The Barotropic System In Mpas-omentioning

confidence: 99%

Section: Linear Iterative Solversmentioning

confidence: 99%

See 3 more Smart Citations

An implicit barotropic mode solver for MPAS-ocean using a modern Fortran solver interface

Kang,

Tuminaro,

Prokopenko

et al. 2023

The International Journal of High Performance Computing Applica

Self Cite

View full text Add to dashboard Cite

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A nonhydrostatic formulation for MPAS-Ocean

Calandrini,

Engwirda,

Van Roekel

2024

Preprint

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Abstract. The Model for Prediction Across Scales-Ocean (MPAS-Ocean) is an open-source, global ocean model and is one component of a family of climate models within the MPAS framework, including atmosphere, sea-ice, and land-ice models. In this work, a new formulation for the ocean model is presented that solves the nonhydrostatic, incompressible Boussinesq equations on an unstructured, staggered, z-level grid. The introduction of this nonhydrostatic capability is necessary for the resolution of internal wave dynamics and large eddy simulations. Compared to the standard, hydrostatic formulation, a nonhydrostatic pressure solver and a vertical momentum equation are added, where the PETSc (Portable Extensible Toolkit for Scientific Computation) library is used for the inversion of a large sparse system for the nonhydrostatic pressure. Numerical results on a stratified seiche, internal solitary wave, overflow and lock-exchange test cases are presented, and the parallel efficiency of the code is evaluated using up to 128 processors.

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wavetrisk-2.1: an adaptive dynamical core for ocean modelling

Kevlahan

Lemarié

2022

Geosci. Model Dev.

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Abstract. This paper introduces wavetrisk-2.1 (i.e. wavetrisk-ocean), an incompressible version of the atmosphere model wavetrisk-1.x with free surface. This new model is built on the same wavelet-based dynamically adaptive core as wavetrisk, which itself uses dynamico's mimetic vector-invariant multilayer rotating shallow water formulation. Both codes use a Lagrangian vertical coordinate with conservative remapping. The ocean variant solves the incompressible multilayer shallow water equations with inhomogeneous density layers. Time integration uses barotropic–baroclinic mode splitting via an semi-implicit free surface formulation, which is about 34–44 times faster than an unsplit explicit time-stepping. The barotropic and baroclinic estimates of the free surface are reconciled at each time step using layer dilation. No slip boundary conditions at coastlines are approximated using volume penalization. The vertical eddy viscosity and diffusivity coefficients are computed from a closure model based on turbulent kinetic energy (TKE). Results are presented for a standard set of ocean model test cases adapted to the sphere (seamount, upwelling and baroclinic turbulence). An innovative feature of wavetrisk-ocean is that it could be coupled easily to the wavetrisk atmosphere model, thus providing a first building block toward an integrated Earth system model using a consistent modelling framework with dynamic mesh adaptivity and mimetic properties.

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A Scalable Semi‐Implicit Barotropic Mode Solver for the MPAS‐Ocean

Cited by 5 publications

References 64 publications

An implicit barotropic mode solver for MPAS-ocean using a modern Fortran solver interface

An implicit barotropic mode solver for MPAS-ocean using a modern Fortran solver interface

A nonhydrostatic formulation for MPAS-Ocean

wavetrisk-2.1: an adaptive dynamical core for ocean modelling

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