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# 2023 Annual PETSc Meeting

June 5-7, 2023, at the Hermann Hall Conference Center in the Hermann Ballroom (when you enter the Hermann Hall building through the main entrance walk straight back to the rear of the building and take a right) (3241 South Federal Street, Chicago, IL) on the campus of The Illinois Institute of Technology (IIT) in Chicago. Easy access from the hotels via the Chicago Elevated Green or Red Lines. Parking use B5 (32nd & Federal St.).

Please test for Covid before attending the meeting and mask while traveling to the meeting.

In addition to a newbie user tutorial and a Newbie Developer Workshop, the meeting will include a “speed dating” session where users can ask questions of developers (and each other) about technical details of their particular simulations. Finally, the meeting will be interspersed with mini-tutorials that will dive into particular aspects of PETSc that users may not be familiar with.

## Meeting times

- Monday, June 5: 1 pm to 5:30 pm

- Tuesday, June 6: 10:15 am to 5:30 pm

- Wednesday, June 7: 9 am to 3 pm

PETSc newbie user lightning tutorial:

- Monday, June 5: 10 am to 12 pm

PETSc Newbie Developer Workshop

- Tuesday, June 6: 9 am to 10 am

## Registration

Please register at EventBrite to save your seat. 100-dollar registration fee for breaks and lunches; this can be skipped if you cannot afford it.

## Submit a presentation

Submit an abstract by May 1st (but preferably now) to be included in the schedule. We welcome talks from all perspectives, including those who

- contribute to PETSc,

- use PETSc in their applications or libraries,

- develop the libraries and packages called from PETSc, and even

- those who are curious about using PETSc in their applications.

## Suggested hotels

- Receive IIT hotel discounts.

- More Expensive

  - Hilton Chicago 720 S Michigan Ave, Chicago

  - Hotel Blake, an Ascend Hotel Collection Member 500 S Dearborn St, Chicago, IL 60605

  - The Blackstone, Autograph Collection 636 South Michigan Avenue Lobby Entrance On, E Balbo Dr, Chicago

- Inexpensive

  - Travelodge by Wyndham Downtown Chicago 65 E Harrison St, Chicago

  - The Congress Plaza Hotel & Convention Center 520 S Michigan Ave, Chicago

  - Hilton Garden Inn Chicago Downtown South Loop 55 E 11th St, Chicago

## Agenda

### Monday, June 5

Time | Title | Speaker
--- | --- | ---
10:00 am | Newbie tutorial (Slides, Video) |
11:30 am | Follow-up questions and meetings |
12:00 am | Lunch for tutorial attendees and early arrivees |
1:00 pm | Some thoughts on the future of PETSc (Slides, Video) | [Barry Smith]
1:30 pm | A new nonhydrostatic capability for MPAS-Ocean (Slides, Video) | [Sara Calandrini]
2:00 pm | MultiFlow: A coupled balanced-force framework to solve multiphase flows in arbitrary domains (Slides, Video) | [Berend van Wachem]
2:30 pm | Mini tutorial: PETSc and PyTorch interoperability (Slides, Video, IPython code) | [Hong Zhang (Mr.)]
2:45 pm | Coffee Break |
3:00 pm | Towards enabling digital twins capabilities for a cloud chamber (slides and video unavailable) | [Vanessa Lopez-Marrero]
3:30 pm | PETSc ROCKS (Slides, Video) | [David May]
4:00 pm | Software Development and Deployment Including PETSc (Slides, Video) | [Tim Steinhoff]
4:30 pm | Multiscale, Multiphysics Simulation Through Application Composition Using MOOSE (Slides, Video) | [Derek Gaston]
5:00 pm | PETSc Newton Trust-Region for Simulating Large-scale Engineered Subsurface Systems with PFLOTRAN (Slides) | [Heeho Park]
5:30 pm | End of first day |

### Tuesday, June 6

Time | Title | Speaker
--- | --- | ---
9:00 am | Newbie Developer Workshop (optional) |
10:00 am | Coffee Break |
10:15 am | Experiences in solving nonlinear eigenvalue problems with SLEPc (Slides, Video) | [Jose E. Roman]
10:45 am | MPI Multiply Threads (Slides, Video) | [Hui Zhou]
11:15 am | Mini tutorial: PETSc on the GPU (Slides, Video) | [Junchao Zhang]
11:30 am | AMD GPU benchmarking, documentation, and roadmap (Slides, video unavailable) | [Justin Chang]
12:00 pm | Lunch |
1:00 pm | Mini tutorial: petsc4py (Slides, Video) | [Stefano Zampini]
1:15 pm | Transparent Asynchronous Compute Made Easy With PETSc (Slides, Video) | [Jacob Faibussowitsch]
1:45 pm | Using Kokkos Ecosystem with PETSc on modern architectures (Slides) | [Luc Berger-Vergiat]
2:15 pm | Intel oneAPI Math Kernel Library, what’s new and what’s next? (Slides, Video) | [Spencer Patty]
2:45 pm | Mini tutorial: DMPlex (Video, slides unavailable) | [Matt Knepley]
3:00 pm | Coffee Break |
3:15 pm | Scalable cloud-native thermo-mechanical solvers using PETSc (slides and video unavailable) | [Ashish Patel]
3:45 pm | A mimetic finite difference based quasi-static magnetohydrodynamic solver for force-free plasmas in tokamak disruptions (Slides, Video) | [Zakariae Jorti]
4:15 pm | High-order FEM implementation in AMReX using PETSc (Slides, Video) | [Alex Grant]
4:45 pm | An Immersed Boundary method for Elastic Bodies Using PETSc (Slides, Video) | [Mohamad Ibrahim Cheikh]
5:15 pm | Mini tutorial: DMNetwork (Slides, Video) | [Hong Zhang (Ms.)]
5:30 pm | End of second day |

### Wednesday, June 7

Time | Title | Speaker
--- | --- | ---
9:00 am | XGCm: An Unstructured Mesh Gyrokinetic Particle-in-cell Code for Exascale Fusion Plasma Simulations (Slides, Video) | [Chonglin Zhang]
9:30 am | PETSc-PIC: A Structure-Preserving Particle-In-Cell Method for Electrostatic Solves (Slides, Video) | [Daniel Finn]
9:57 am | Landau Collisions in the Particle Basis with PETSc-PIC (Slides, Video) | [Joseph Pusztay]
10:15 am | Coffee Break |
10:30 am | Mini tutorial: DMSwarm (Slides, Video) | [Joseph Pusztay*][joseph pusztay*]
10:45 am | Scalable Riemann Solvers with the Discontinuous Galerkin Method for Hyperbolic Network Simulation (Slides, Video) | [Aidan Hamilton]
11:15 am | Numerical upscaling of network models using PETSc (Slides, Video) | [Maria Vasilyeva]
11:45 am | Mini tutorial: TaoADMM (Slides, Video) | [Hansol Suh]
12:00 am | Lunch |
1:00 pm | PETSc in the Ionosphere (Slides, Video) | [Matt Young]
1:30 pm | From the trenches: porting mef90 (Slides, Video) | [Blaise Bourdin]
2:00 pm | PERMON library for quadratic programming (Slides, Video) | [Jakub Kruzik]
2:22 pm | Distributed Machine Learning for Natural Hazard Applications Using PERMON (Slides, Video) | [Marek Pecha]
2:45 pm | Wrap up |
3:00 pm | End of meeting |

## Newbie Developer Workshop

Tuesday, June 6, at 9 am. Some of the topics to be covered.

- Exploring the developer documentation

- PETSc Developers Communication Channels

- PETSc Git branch organization

- Contributing to PETSc

  - Starting a merge request (MR)

  - Submitting and monitoring a MR

  - GitLab CI pipelines

  - PETSc style guide

- Reviewing someone else’s MR

- Adding new Fortran and Python function bindings

- PETSc’s

  - configure system

  - compiler system, and

  - testing system including the GitLab CI

- Any other topics requested by potential contributors

## Abstracts

Using Kokkos Ecosystem with PETSc on modern architectures

Luc Berger-Vergiat

Sandia National Laboratories

Supercomputers increasingly rely on GPUs to achieve high throughput while maintaining a reasonable power consumption. Consequently, scientific applications are adapting to this new environment, and new algorithms are designed to leverage the high concurrency of GPUs. In this presentation, I will show how the Kokkos Ecosystem can help alleviate some of the difficulties associated with support for multiple CPU/GPU architectures. I will also show some results using the Kokkos and Kokkos kernels libraries with PETSc on modern architectures.

From the trenches: porting mef90

Blaise Bourdin

McMaster University

mef90 is a distributed three-dimensional unstructured finite-element implementation of various phase-field models of fracture. In this talk, I will share the experience gained while porting mef90 from PETSc 3.3 to 3.18.

A new non-hydrostatic capability for MPAS-Ocean

Sara Calandrini

, Darren Engwirda, Luke Van Roekel

Los Alamos National Laboratory

The Model for Prediction Across Scales-Ocean (MPAS-Ocean) is an open-source, global ocean model and is one component within the Department of Energy’s E3SM framework, which includes atmosphere, sea ice, and land-ice models. In this work, a new formulation for the ocean model is presented that solves the non-hydrostatic, incompressible Boussinesq equations on unstructured meshes. The introduction of this non-hydrostatic capability is necessary for the representation of fine-scale dynamical processes, including resolution of internal wave dynamics and large eddy simulations. Compared to the standard hydrostatic formulation, a non-hydrostatic 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 comparing the solutions of the hydrostatic and non-hydrostatic models are presented, and the parallel efficiency and accuracy of the time-stepper are evaluated.

AMD GPU benchmarking, documentation, and roadmap

Justin Chang

AMD Inc.

This talk comprises three parts. First, we present an overview of some relatively new training documentation like the “AMD lab notes” to enable current and potential users of AMD GPUs into getting the best experience out of their applications or algorithms. Second, we briefly discuss implementation details regarding the PETSc HIP backend introduced into the PETSc library late last year and present some performance benchmarking data on some of the AMD hardware. Lastly, we give a preview of the upcoming MI300 series APU and how software developers can prepare to leverage this new type of accelerator.

An Immersed Boundary method for Elastic Bodies Using PETSc

Mohamad Ibrahim Cheikh

, Konstantin Doubrovinski

Doubrovinski Lab, The University of Texas Southwestern Medical Center

This study presents a parallel implementation of an immersed boundary method code using the PETSc distributed memory module. This work aims to simulate a complex developmental process that occurs in the early stages of embryonic development, which involves the transformation of the embryo into a multilayered and multidimensional structure. To accomplish this, the researchers used the PETSc parallel module to solve a linear system for the Eulerian fluid dynamics while simultaneously coupling it with a deforming Lagrangian elastic body to model the deformable embryonic tissue. This approach allows for a detailed simulation of the interaction between the fluid and the tissue, which is critical for accurately modeling the developmental process. Overall, this work highlights the potential of the immersed boundary method and parallel computing techniques for simulating complex physical phenomena.

Transparent Asynchronous Compute Made Easy With PETSc

Jacob Faibussowitch

Argonne National Laboratory

Asynchronous GPU computing has historically been difficult to integrate scalably at the library level. We provide an update on recent work implementing a fully asynchronous framework in PETSc. We give detailed performance comparisons and provide a demo to showcase the proposed model’s effectiveness and ease of use.

PETSc-PIC: A Structure-Preserving Particle-In-Cell Method for Electrostatic Solves

Daniel Finn

University at Buffalo

Numerical solutions to the Vlasov-Poisson equations have important applications in the fields of plasma physics, solar physics, and cosmology. The goal of this research is to develop a structure-preserving, electrostatic and gravitational Vlasov-Poisson(-Landau) model using the Portable, Extensible Toolkit for Scientific Computation (PETSc) and study the presence of Landau damping in a variety of systems, such as thermonuclear fusion reactors and galactic dynamics. The PETSc Particle-In-Cell (PETSc-PIC) model is a highly scalable, structure-preserving PIC method with multigrid capabilities. In the PIC method, a hybrid discretization is constructed with a grid of finitely supported basis functions to represent the electric, magnetic, and/or gravitational fields, and a distribution of delta functions to represent the particle field. Collisions are added to the formulation using a particle-basis Landau collision operator recently added to the PETSc library.

Multiscale, Multiphysics Simulation Through Application Composition Using MOOSE

Derek Gaston

Idaho National Laboratory

Eight years ago, at the PETSc 20 meeting, I introduced the idea of “Simplifying Multiphysics Through Application Composition” – the idea that physics applications can be built in such a way that they can instantly be combined to tackle complicated multiphysics problems. This talk will serve as an update on those plans. I will detail the evolution of that idea, how we’re using it in practice, how well it’s working, and where we’re going next. Motivating examples will be drawn from nuclear engineering, and practical aspects, such as testing, will be explored.

High-order FEM implementation in AMReX using PETSc

Alex Grant

, Karthik Chockalingam, Xiaohu Guo

Science and Technology Facilities Council (STFC), UK

AMReX is a C++ block-structured framework for adaptive mesh refinement, typically used for finite difference or finite volume codes. We describe a first attempt at a finite element implementation in AMReX using PETSc. AMReX splits the domain of uniform elements into rectangular boxes at each refinement level, with higher levels overlapping rather than replacing lower levels and with each level solved independently. AMReX boxes can be cell-centered or nodal; we use cell centered boxes to represent the geometry and mesh and nodal boxes to identify nodes to constrain and store results for visualization. We convert AMReX’s independent spatial indices into a single global index, then use MATMPIAIJ to assemble the system matrix per refinement level. In an unstructured grid, isoparametric mapping is required for each element; using a structured grid avoids both this and indirect addressing, which provides significant potential performance advantages. We have solved time-dependent parabolic equations and seen performance gains compared to unstructured finite elements. Further developments will include arbitrary higher-order schemes and multi-level hp refinement with arbitrary hanging nodes. PETSc uses AMReX domain decomposition to partition the matrix and right-hand vectors. For each higher level, not all of the domain will be refined, but AMReX’s indices cover the whole space - this poses an indexing challenge and can lead to over-allocation of memory. It is still to be explored whether DM data structures would provide a benefit over MATMPIAIJ.

Scalable Riemann Solvers with the Discontinuous Galerkin Method for Hyperbolic Network Simulation

Aidan Hamilton

, Jing-Mei Qiu, Hong Zhang

University of Delaware

We develop highly efficient and effective computational algorithms and simulation tools for fluid simulations on a network. The mathematical models are a set of hyperbolic conservation laws on the edges of a network, as well as coupling conditions on junctions of a network. For example, the shallow water system, together with flux balance and continuity conditions at river intersections, model water flows on a river network. The computationally accurate and robust discontinuous Galerkin methods, coupled with explicit strong-stability preserving Runge-Kutta methods, are implemented for simulations on network edges. Meanwhile, linear and nonlinear scalable Riemann solvers are being developed and implemented at network vertices. These network simulations result in tools built using PETSc and DMNetwork software libraries for the scientific community in general. Simulation results of a shallow water system on a Mississippi river network with over one billion network variables are performed on an extreme- scale computer using up to 8,192 processors with an optimal parallel efficiency. Further potential applications include traffic flow simulations on a highway network and blood flow simulations on an arterial network, among many others

A mimetic finite difference based quasi-static magnetohydrodynamic solver for force-free plasmas in tokamak disruptions

Zakariae Jorti

, Qi Tang, Konstantin Lipnikov, Xianzhu Tang

Los Alamos National Laboratory

Force-free plasmas are a good approximation in the low-beta case, where the plasma pressure is tiny compared with the magnetic pressure. On time scales long compared with the transit time of Alfvén waves, the evolution of a force-free plasma is most efficiently described by a quasi-static magnetohydrodynamic (MHD) model, which ignores the plasma inertia. In this work, we consider a regularized quasi-static MHD model for force-free plasmas in tokamak disruptions and propose a mimetic finite difference (MFD) algorithm, which is targeted at applications such as the cold vertical displacement event (VDE) of a major disruption in an ITER-like tokamak reactor. In the case of whole device modeling, we further consider the two sub-domains of the plasma region and wall region and their coupling through an interface condition. We develop a parallel, fully implicit, and scalable MFD solver based on PETSc and its DMStag data structure to discretize the five-field quasi-static perpendicular plasma dynamics model on a 3D structured mesh. The MFD spatial discretization is coupled with a fully implicit DIRK scheme. The full algorithm exactly preserves the divergence-free condition of the magnetic field under a generalized Ohm’s law. The preconditioner employed is a four-level fieldsplit preconditioner, created by combining separate preconditioners for individual fields, that calls multigrid or direct solvers for sub-blocks or exact factorization on the separate fields. The numerical results confirm the divergence-free constraint is strongly satisfied and demonstrate the performance of the fieldsplit preconditioner and overall algorithm. The simulation of ITER VDE cases over the actual plasma current diffusion time is also presented.

PERMON library for quadratic programming

Jakub Kruzik

, Marek Pecha, David Horak

VSB - Technical University of Ostrava, Czechia

PERMON (Parallel, Efficient, Robust, Modular, Object-oriented, Numerical) is a library based on PETSc for solving quadratic programming (QP) problems. We will present PERMON usage on our implementation of the FETI (finite element tearing and interconnecting) method. This FETI implementation involves a chain of QP transformations, such as dualization, which simplifies a given QP. We will also discuss some useful options, like viewing Karush-Kuhn-Tucker (optimality) conditions for each QP in the chain. Finally, we will showcase some QP applications solved by PERMON, such as the solution of contact problems for hydro-mechanical problems with discrete fracture networks or the solution of support vector machines using the PermonSVM module.

Towards enabling digital twins capabilities for a cloud chamber

Vanessa Lopez-Marrero

, Kwangmin Yu, Tao Zhang, Mohammad Atif, Abdullah Al Muti Sharfuddin, Fan Yang, Yangang Liu, Meifeng Lin, Foluso Ladeinde, Lingda Li

Brookhaven National Laboratory

Particle-resolved direct numerical simulations (PR-DNS), which resolve not only the smallest turbulent eddies but also track the development and the motion of individual particles, are an essential tool for studying aerosol-cloud-turbulence interactions. For instance, PR-DNS may complement experimental facilities designed to study key physical processes in a controlled environment and therefore serve as digital twins for such cloud chambers. In this talk, we will present our ongoing work aimed at enabling the use of PR-DNS for this purpose. We will describe the physical model used, which consists of a set of fluid dynamics equations for air velocity, temperature, and humidity coupled with a set of equations for particle (i.e., droplet) growth/tracing. The numerical method used to solve the model, which employs PETSc solvers in its implementation, will be discussed, as well as our current efforts to assess performance and scalability of the numerical solver.

PETSc ROCKS

David May

University of California, San Diego

The field of Geodynamics is concerned with understanding the deformation history of the solid Earth over millions to billions of year time scales. The infeasibility of extracting a spatially and temporally complete geological record based on rocks that are currently exposed at the surface of the Earth compels many geodynamists to employ computational simulations of geological processes.

In this presentation I will discuss several geodynamic software packages which utilize PETSc. I intend to highlight how PETSc has played an important role in enabling and advancing state-of-the-art in geodynamic software. I will also summarize my own experiences and observations of how geodynamic-specific functionality has driven the development of new general-purpose PETSc functionality.

PETSc Newton Trust-Region for Simulating Large-scale Engineered Subsurface Systems with PFLOTRAN

Heeho Park

, Glenn Hammond, Albert Valocchi

Sandia National Laboratories

Modeling large-scale engineered subsurface systems entails significant additional numerical challenges. For nuclear waste repository, the challenges arise from: (a) the need to accurately represent both the waste form processes and shafts, tunnel, and barriers at the small spatial scale and the large-scale transport processes throughout geological formations; (b) the strong contrast in material properties such as porosity and permeability, and the nonlinear constitutive relations for multiphase flow; (c) the decay of high level nuclear wastes cause nearby water to boil off into steam leading to dry-out. These can lead to an ill-conditioned Jacobian matrix and non-convergence with Newton’s method due to discontinuous nonlinearity in constitutive models.

We apply the open-source simulator PFLOTRAN which employs a FV discretization and uses the PETSc parallel framework. We implement within PETSc the general-purpose nonlinear solver, Newton trust-region dogleg Cauchy (NTRDC) and Newton trust-region (NTR) to demonstrate the effectiveness of these advanced solvers. The results demonstrate speed-up compared to the default solvers of PETSc and complete simulations that were never completed with them.

SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.

Scalable cloud-native thermo-mechanical solvers using PETSc

Ashish Patel

, Jeremy Theler, Francesc Levrero-Florencio, Nabil Abboud, Mohammad Sarraf Joshaghani, Scott McClennan

Ansys, Inc.

This talk presents how the Ansys OnScale team uses PETSc to develop finite element-based thermo-mechanical solvers for scalable nonlinear simulations on the cloud. We will first provide an overview of features available in the solver and then discuss how some of the PETSc objects, like DMPlex and TS, have helped us speed up our development process. We will also talk about the workarounds we have incorporated to address the current limitations of some of the functions from DMPlex for our use cases involving multi-point constraints and curved elements. Finally, we demonstrate how PETSc’s linear solvers scale on multi-node cloud instances.

Intel oneAPI Math Kernel Library, what’s new and what’s next?

Spencer Patty

Intel Corporation

This talk provides an overview of Intel® oneAPI Math Kernel Library (oneMKL) product and software for supporting optimized math routines for both Intel CPUs and GPUs. Given that PETSc already utilizes several BLAS/LAPACK/Sparse BLAS routines from oneMKL for Intel CPU and as part of the Aurora project with Argonne, we discuss the use of OpenMP offload APIs for Intel GPUs. We explore software and hardware improvements for better sparse linear algebra performance and have an informal discussion of how to further support the PETSc community.

Distributed Machine Learning for Natural Hazard Applications Using PERMON

Marek Pecha

, David Horak, Richard Tran Mills, Zachary Langford

VSB – Technical University of Ostrava, Czechia

We will present a software solution for distributed machine learning supporting computation on multiple GPUs running on the top of the PETSc framework, which we will demonstrate in applications related to natural hazard localizations and detections employing supervised uncertainties modeling. It is called PERMON and is designed for convex optimization using quadratic programming, and its extension PermonSVM implements maximal-margin classifier approaches associated with support vector machines (SVMs). Although deep learning (DL) is getting popular in recent years, SVMs are still applicable. However, unlike DL, the SVM approach requires additional feature engineering or feature selection. We will present our workflow and show how to achieve reasonable models for the application related to wildfire localization in Alaska.

Landau Collisions in the Particle Basis with PETSc-PIC

Joseph Pusztay

, Matt Knepley, Mark Adams

University at Buffalo

The kinetic description of plasma encompasses the fine scale interaction of the various bodies that it is comprised of, and applies to a litany of experiments ranging from the laboratory magnetically confined fusion plasma, to the scale of the solar corona. Of great import to these descriptions are collisions in the grazing limit, which transfer momentum between components of the plasma. Until recently, these have best been described conservatively by finite element discretizations of the Landau collision integral. In recent years a particle discretization has been proven to preserve the appropriate eigenfunctions of the system, as well as physically relevant quantities. I present here the recent work on a purely particle discretized Landau collision operator which preserves mass, momentum, and energy, with associated accuracy benchmarks in PETSc.

Experiences in solving nonlinear eigenvalue problems with SLEPc

Jose E. Roman

Universitat Politècnica de València

One of the unique features of SLEPc is the module for the general nonlinear eigenvalue problem (NEP), where we want to compute a few eigenvalues and corresponding eigenvectors of a large-scale parameter-dependent matrix T(lambda). In this talk, we will illustrate the use of NEP in the context of two applications, one of them coming from the characterization of resonances in nanophotonic devices, and the other one from a problem in aeroacoustics.

Some thoughts on the future of PETSc:

Barry Smith

Flatiron Institute

How will PETSc evolve and grow in the future? How can PETSc algorithms and simulations be integrated into the emerging world of machine learning and deep neural networks? I will provide an informal discussion of these topics and my thoughts.

Software Development and Deployment Including PETSc

Tim Steinhoff

, Volker Jacht

Gesellschaft für Anlagen- und Reaktorsicherheit (GRS), Germany

Once it is decided that PETSc shall handle certain numerical subtasks in your software the question may arise about how to smoothly incorporate PETSc into the overall software development and deployment processes. In this talk, we present our approach how to handle such a situation for the code family AC2 which is developed and distributed by GRS. AC2 is used to simulate the behavior of nuclear reactors during operation, transients, design basis and beyond design basis accidents up to radioactive releases to the environment. The talk addresses our experiences, what challenges had to be overcome, and how we make use of GitLab, CMake, and Docker techniques to establish clean incorporation of PETSc into our software development cycle.

TaoADMM

Hansol Suh

Argonne National Laboratory

In this tutorial, we will be giving an introduction to ADMM algorithm on TAO. It will include walking through ADMM algorithm with some real-life example, and tips on setting up the framework to solve ADMM on PETSc/TAO.

Numerical upscaling of network models using PETSc

Maria Vasilyeva

Texas A&M University-Corpus Christi

Multiphysics models on large networks are used in many applications, for example, pore network models in reservoir simulation, epidemiological models of disease spread, ecological models on multispecies interaction, medical applications such as multiscale multidimensional simulations of blood flow, etc. This work presents the construction of the numerical upscaling and multiscale method for network models. An accurate coarse-scale approximation is generated by solving local problems in sub-networks. Numerical implementation of the network model is performed based on the PETSc DMNetwork framework. Results are presented for square and random heterogeneous networks generated by OpenPNM.

MultiFlow: A coupled balanced-force framework to solve multiphase flows in arbitrary domains

Berend van Wachem

, Fabien Evrard

University of Magdeburg, Germany

Since 2000, we have been working on a finite-volume numerical framework “MultiFlow ” to predict multiphase flows in arbitrary domains by solving various flavors of the incompressible and compressible Navier-Stokes equations using PETSc. This framework enables the simulation of creeping, laminar and turbulent flows with droplets and/or particles at various scales. It relies on a collocated variable arrangement of the unknown variables and momentum-weighted-interpolation to determine the fluxes at the cell faces to couple velocity and pressure. To maximize robustness, the governing flow equations are solved in a coupled fashion, i.e., as part of a single equation system involving all flow variables. Various modules are available within the code in addition to its core flow solver, allowing it to model interfacial and particulate flows at various flow regimes and scales. The framework heavily relies on the PETSc library not only to solve the system of governing equations but also for the handling of unknown variables, parallelization of the computational domain, and exchange of data over processor boundaries. We are now in the 3rd generation of our code, currently using a combination of DMDA, and DMPlex with DMForest/p4est frameworks to allow for the adaptive octree refinement of the computational mesh. In this contribution, we will present the details of the discretization and the parallel implementation of our framework and describe its interconnection with the PETSc library. We will then present some applications of our framework, simulating multiphase flows at various scales, flows regimes, and resolutions. During this contribution, we will also discuss our framework’s challenges and future objectives.

PETSc in the Ionosphere

Matt Young

University of New Hampshire

A planet’s ionosphere is the region of its atmosphere where a fraction of the constituent atoms or molecules have separated into positive ions and electrons. Earth’s ionosphere extends from roughly 85 km during the day (higher at night) to the edge of space. This partially ionized regime exhibits collective behavior and supports electromagnetic phenomena that do not exist in the neutral (i.e., unionized) atmosphere. Furthermore, the abundance of neutral atoms and molecules leads to phenomena that do not exist in the fully ionized space environment. In a relatively narrow altitude range of Earth’s ionosphere called the “E region”, electrons behave as typical charged particles – moving in response to combined electric and magnetic fields – while ions collide too frequently with neutral molecules to respond to the magnetic field. This difference leads to the Farley-Buneman instability when the local electric field is strong enough. The Farley-Buneman instability regularly produces irregularities in the charged-particle densities that are strong enough to reflect radio signals. Recent research suggests that fully developed turbulent structures can disrupt GPS communication.

The Electrostatic Parallel Particle-in-Cell (EPPIC) numerical simulation self-consistently models instability growth and evolution in the E-region ionosphere. The simulation includes a hybrid mode that treats electrons as a fluid and treats ions as particles. The particular fluid electron model requires the solution of an elliptic partial differential equation for the electrostatic potential at each time step, which we represent as a linear system that the simulation solves with PETSc. This presentation will describe the original development of the 2D hybrid simulation, previous results, recent efforts to extend to 3D, and implications for modeling GPS scintillation.

The Electrostatic Parallel Particle-in-Cell (EPPIC) numerical simulation self-consistently models instability growth and evolution in the E-region ionosphere. The simulation includes a hybrid mode that treats electrons as a fluid and treats ions as particles. The particular fluid electron model requires the solution of an elliptic partial differential equation for the electrostatic potential at each time step, which we represent as a linear system that the simulation solves with PETSc. This presentation will describe the original development of the 2D hybrid simulation, previous results, recently efforts to extend to 3D, and implications to modeling GPS scintillation.

XGCm: An Unstructured Mesh Gyrokinetic Particle-in-cell Code for Exascale Fusion Plasma Simulations

Chonglin Zhang

, Cameron W. Smith, Mark S. Shephard

Rensselaer Polytechnic Institute (RPI)

We report the development of XGCm, a new distributed unstructured mesh gyrokinetic particle-in-cell (PIC) code, short for x-point included gyrokinetic code mesh-based. The code adopts the physical algorithms of the well-established XGC code. It is intended as a testbed for experimenting with new numerical and computational algorithms, which can eventually be adopted in XGC and other PIC codes. XGCm is developed on top of several open-source libraries, including Kokkos, PETSc, Omega, and PUMIPic. Omega and PUMIPic rely on Kokkos to interact with the GPU accelerator, while PETSc solves the gyrokinetic Poisson equation on either CPU or GPU. We first discuss the numerical algorithms of our mesh-centric approach for performing PIC calculations. We then present a code validation study using the cyclone base case with ion temperature gradient turbulence (case 5 from Burckel, etc. Journal of Physics: Conference Series 260, 2010, 012006). Finally, we discuss the performance of XGCm and present weak scaling results using up to the full system (27,648 GPUs) of the Oak Ridge National Laboratory’s Summit supercomputer. Overall, XGCm executes all PIC operations on the GPU accelerators and exhibits good performance and portability.

PETSc DMNetwork: A Library for Scalable Network PDE-Based Multiphysics Simulation

Hong Zhang (Ms.)

Argonne National Laboratory, Illinois Institute of Technology

We present DMNetwork, a high-level set of routines included in the PETSc library for the simulation of multiphysics phenomena over large-scale networked systems. The library aims at applications with networked structures like those in electrical, water, and traffic distribution systems. DMNetwork provides data and topology management, parallelization for multiphysics systems over a network, and hierarchical and composable solvers to exploit the problem structure. DMNetwork eases the simulation development cycle by providing the necessary infrastructure to define and query the network components through simple abstractions.

MPI Multiply Threads

Hui Zhou

Argonne National Laboratory

In the traditional MPI+Thread programming paradigm, MPI and OpenMP each form their own parallelization. MPI is unaware of the thread context. The requirement of thread safety and message ordering forces MPI library to blindly add critical sections, unnecessarily serializing the code. On the other hand, OpenMP cannot use MPI for inter-thread communications. Developers often need hand-roll algorithms for collective operations and non-blocking synchronizations.

MPICH recently added a few extensions to address the root issues in MPI+Thread. The first extension, MPIX stream, allows applications to explicitly pass the thread context into MPI. The second extension, thread communicator, allows individual threads in an OpenMP parallel region to use MPI for inter-thread communications. In particular, this allows an OpenMP program to use PETSc within a parallel region.

Instead of MPI+Thread, we refer to this new pattern as MPI x Thread.

PETSc on the GPU

Junchao Zhang

Argonne National Laboratory

In this mini-tutorial, we will briefly introduce the GPU backends of PETSc and how to configure, build, run and profile PETSc on GPUs. We also talk about how to port your PETSc code to GPUs.

PETSc and PyTorch Interoperability

Hong Zhang (Mr.)

Argonne National Laboratory

In this mini-tutorial, we will introduce: How to convert between PETSc vectors/matrices and PyTorch tensors; How to generate Jacobian or action of Jacobian with PyTorch and use it in PETSc; How to use PETSc and PyTorch for solving ODEs and training neural ODEs.

petsc4py

Stefano Zampini

King Abdullah University of Science and Technology (KAUST)

In this mini-tutorial, we will introduce the Python binding of PETSc.

DMPlex

Matt Knepley

University at Buffalo

In this mini-tutorial, we will introduce the DMPlex class in PETSc.

DMSwarm

Joseph Pusztay

University at Buffalo

In this mini-tutorial, we will introduce the DMSwarm class in PETSc.