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This paper presents a flexible framework for parallel and easy-to-implement topology optimization using the Portable and Extendable Toolkit for Scientific Computing (PETSc). The presented framework is based on a standardized, and freely available library and in the published form it solves the minimum compliance problem on structured grids, using standard FEM and filtering techniques. For completeness a parallel implementation of the Method of Moving Asymptotes is included as well. The capabilities are exemplified by minimum compliance and homogenization problems. In both cases the unprecedented fine discretization reveals new design features, providing novel insight. The code can be downloaded from www.topopt.dtu.dk/PETSc .

The aim of this work is to introduce a unified description of topology optimization (TO) methods, which modularizes and generalizes all TO methods, both density based and boundary based. This unified description allows for the implementation of a reusable modular TO software, ParaLeSTO, which specializes in level set TO (LSTO). In addition, we use this software as a means to propose a guideline for research software metadata in the TO community. The proposed guideline for the research software metadata is based on the FAIR principles for research software, which focuses on improving the findability, accessibility, interoperability, and reusability of research software and its metadata. The modularized TO framework separates the analysis, which solves the state equations and does the sensitivity analysis, and the design modification, which represents and modifies the design. Mapping is then used to interface between the two. We demonstrate the interoperability and reusability of this framework through numerical examples.

Enormous advances in physics of complex fluids/soft matter over last decades have rapidly transformed traditional industrial sectors in foods, personal care products, pharmaceuticals, paints, lubricants, ceramics, polymers, liquid crystals, high performance fibers, oil exploration and production into a digital era of formulation design and precision control over processing conditions from molecular viewpoint, and fertilizing a new industrial revolution. Development of high performance viscoelastic fluid solvers is of great significance for large scale digital manufacturing. In the present work, a portable and extensible scientific computing (PETSc) toolbox has been successfully integrated into the popular OpenFOAM CFD toolbox for carrying out large scale parallel computing of Turbulent Drag Reduction ( TDR ) and Elastic Turbulence ( ET ) in the isotropic turbulence flow. Its scalability has been evaluated and compared with the scalability of the OpenFOAM based viscoelastic fluid solvers. The results show that there are significant improvements.

The computational complexity of solving nonlinear support vector machine (SVM) is prohibitive on large-scale data. In particular, this issue becomes very sensitive when the data represents additional difficulties such as highly imbalanced class sizes. Typically, nonlinear kernels produce significantly higher classification quality to linear kernels but introduce extra kernel and model parameters which requires computationally expensive fitting. This increases the quality but also reduces the performance dramatically. We introduce a generalized fast multilevel framework for regular and weighted SVM and discuss several versions of its algorithmic components that lead to a good trade-off between quality and time. Our framework is implemented using PETSc which allows an easy integration with scientific computing tasks. The experimental results demonstrate significant speed up compared to the state-of-the-art nonlinear SVM libraries. Reproducibility: our source code, documentation and parameters are available at https://github.com/esadr/mlsvm.

This paper presents a Python wrapper and extended functionality of the parallel topology optimization framework introduced by Aage et al. (Topology optimization using PETSc: an easy-to-use, fully parallel, open source topology optimization framework. Struct Multidiscip Optim 51(3):565–572, 2015). The Python interface, which simplifies the problem definition, is intended to expand the potential user base and to ease the use of large-scale topology optimization for educational purposes. The functionality of the topology optimization framework is extended to include passive domains and local volume constraints among others, which contributes to its usability to real-world design applications. The functionality is demonstrated via the cantilever beam, bracket and torsion ball examples. Several tests are provided which can be used to verify the proper installation and for evaluating the performance of the user’s system setup. The open-source code is available at https://github.com/thsmit/ , repository TopOpt _ in _ PETSc _ wrapped _ in _ Python .

Battery performance is strongly correlated with electrode microstructure. Electrode materials for lithium-ion batteries have complex microstructure geometries that require millions of degrees of freedom to solve the electrochemical system at the microstructure scale. A fast-iterative solver with an appropriate preconditioner is then required to simulate large representative volume in a reasonable time. In this work, a finite element electrochemical model is developed to resolve the concentration and potential within the electrode active materials and the electrolyte domains at the microstructure scale, with an emphasis on numerical stability and scaling performances. The block Gauss-Seidel (BGS) numerical method is implemented because the system of equations within the electrodes is coupled only through the nonlinear Butler–Volmer equation, which governs the electrochemical reaction at the interface between the domains. The best solution strategy found in this work consists of splitting the system into two blocks—one for the concentration and one for the potential field—and then performing block generalized minimal residual preconditioned with algebraic multigrid, using the FEniCS and the Portable, Extensible Toolkit for Scientific Computation libraries. Significant improvements in terms of time to solution (six times faster) and memory usage (halving) are achieved compared with the MUltifrontal Massively Parallel sparse direct Solver. Additionally, BGS experiences decent strong parallel scaling within the electrode domains. Last, the system of equations is modified to specifically address numerical instability induced by electrolyte depletion, which is particularly valuable for simulating fast-charge scenarios relevant for automotive application.

Co-simulation is a widely used solution to enable global simulation of a modular system via the composition of black-boxed simulators. Among co-simulation methods, the IFOSMONDI implicit iterative algorithm, previously introduced by the authors, enables us to solve the non-linear coupling function while keeping the smoothness of interfaces without introducing a delay. Moreover, it automatically adapts the size of the steps between data exchanges among the subsystems according to the difficulty of solving the coupling constraint. The latter was solved by a fixed-point algorithm, whereas this paper introduces the Jacobian-Free Methods version. Most implementations of Newton-like methods require a jacobian matrix which, except in the Zero-Order-Hold case, can be difficult to compute in the co-simulation context. As IFOSMONDI coupling algorithm uses Hermite interpolation for smoothness enhancement, we propose hereafter a new formulation of the non-linear coupling function including both the values and the time-derivatives of the coupling variables. This formulation is well designed for solving the coupling through jacobian-free Newton-type methods. Consequently, successive function evaluations consist in multiple simulations of the systems on a co-simulation time-step using rollback. The orchestrator-workers structure of the algorithm enables us to combine the PETSc framework on the orchestrator side for the non-linear Newton-type solvers with the parallel integrations of the systems on the workers’ side thanks to MPI processes. Different non-linear methods will be compared to one another and to the original fixed-point implementation on a newly proposed 2-system academic test case with direct feedthrough on both sides. An industrial model will also be considered to investigate the performance of the method.

Ultra-high-voltage (UHV) autotransformers are widely employed in long-distance power transmission systems. Their operation involves complex energy conversion and coupling mechanisms, including high-intensity magnetic induction energy and strong induced currents. From the perspective of power systems and automation control, it is essential to construct a comprehensive equivalent control circuit for UHV autotransformers, integrating the analysis of induced current and magnetic flux density into the domain of analog electronics. Numerical analysis has become a core approach for investigating the external thermal physical characteristics of transformer power and various thermal management strategies. In this paper, the Message Passing Interface (MPI) and Portable, Extensible Toolkit for Scientific Computation (PETSc) parallel computing framework is adopted to compute and analyze the electro-thermal coupling in a UHV autotransformer. The dielectric loss of transformer components is thoroughly examined. A linear numerical simulation method for evaluating dielectric loss is assessed through parallel computation and validated via the design of a three-dimensional coupling model for leakage flux and core temperature rise. The dielectric loss calculation is applied to the transformer. Magnetostriction measurements under rated output power and various current and voltage conditions reveal the correlation between the coupled data and the thermal topology. The MPI-PETSc framework significantly enhances the computational efficiency of three-dimensional electro-thermal coupling problems in UHV autotransformers through distributed computing and efficient numerical solving, making it suitable for large-scale, high-precision engineering simulations.

We describe our software package Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) recently publicly released. BLOPEX is available as a stand-alone serial library, as an external package to PETSc (Portable, Extensible Toolkit for Scientific Computation, a general purpose suite of tools developed by Argonne National Laboratory for the scalable solution of partial differential equations and related problems), and is also built into hypre (High Performance Preconditioners, a scalable linear solvers package developed by Lawrence Livermore National Laboratory). The present BLOPEX release includes only one solver--the Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) method for symmetric eigenvalue problems. hypre provides users with advanced high-quality parallel multigrid preconditioners for linear systems. With BLOPEX, the same preconditioners can now be efficiently used for symmetric eigenvalue problems. PETSc facilitates the integration of independently developed application modules, with strict attention to component interoperability, and makes BLOPEX extremely easy to compile and use with preconditioners that are available via PETSc. We present the LOBPCG algorithm in BLOPEX for hypre and PETSc. We demonstrate numerically the scalability of BLOPEX by testing it on a number of distributed and shared memory parallel systems, including a Beowulf system, SUN Fire 880, an AMD dual-core Opteron workstation, and IBM BlueGene/L supercomputer, using PETSc domain decomposition and hypre multigrid preconditioning. We test BLOPEX on a model problem, the standard 7-point finite-difference approximation of the 3-D Laplacian, with the problem size in the range of$10^5$ - $10^8$ .

The upward trends in renewable energy penetration, cross-border flow volatility and electricity actors’ proliferation pose new challenges in the power system management. Electricity and market operators need to increase collaboration, also in terms of more frequent and detailed system analyses, so as to ensure adequate levels of quality and security of supply. This work proposes a novel distributed load flow solver enabling for better cross border flow analysis and fulfilling possible data ownership and confidentiality arrangements in place among the actors. The model exploits an Inexact Newton Method, the Newton–Krylov–Schwarz method, available in the portable, extensible toolkit for scientific computation (PETSc) libraries. A case-study illustrates a real application of the model for the TSO–TSO (transmission system operator) cross-border operation, analyzing the specific policy context and proposing a test case for a coordinated power flow simulation. The results show the feasibility of performing the distributed calculation remotely, keeping the overall simulation times only a few times slower than locally.