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Optimizations and applications in large-scale scenes of Monte Carlo geometry conversion code CMGC

Nuclear Science and Techniques 2025年第4期36卷 220-232页

作者： Xin Wang Ling-Yu Zhang Xue-Ming Shi Zhen Wu Jun-Li Li Gui-Ming Qin Yuan-Guang Fu CAEP Software Center for High Performance Numerical Simulation Beijing 100088China Institute of Applied Physics and Computational Mathematics Beijing 100088China Department of Engineering Physics Tsinghua UniversityBeijing 100084China

In response to the demand for rapid geometric modeling in Monte Carlo radiation transportation calculations for large-scale and complex geometric scenes,functional improvements,and algorithm optimizations were performed using CAD-to-Monte Carlo geometry conversion(CMGC)*** representation(BRep)to constructive solid geometry(CSG)conversion and visual CSG modeling were combined to address the problem of non-convertible geometries such as spline *** splitting surface assessment method in BRep-to-CSG conversion was optimized to reduce the number of Boolean operations using an Open ***,in turn,reduced the probability of CMGC conversion *** auxiliary surface generation algorithm was optimized to prevent the generation of redundant auxiliary surfaces that cause an excessive decomposition of CAD geometry *** optimizations enhanced the usability and stability of the CMGC model *** was applied successfully to the JMCT transportation calculations for the conceptual designs of five China Fusion Engineering Test Reactor(CFETR)*** rapid replacement of different blanket schemes was achieved based on the baseline CFETR *** geometric solid number of blankets ranged from hundreds to tens of *** correctness of the converted CFETR models using CMGC was verified through comparisons with the MCNP calculation *** CMGC supported radiation field evaluations for a large urban scene and detailed ship *** enabled the rapid conversion of CAD models with thousands of geometric solids into Monte Carlo CSG *** analysis of the JMCT transportation simulation results further demonstrated the accuracy and effectiveness of the CMGC.

关键词： Monte Carlo CAD BRep to CSG CMGC

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A localized orthogonal decomposition strategy for hybrid discontinuous Galerkin methods

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ESAIM: Mathematical Modelling and numerical Analysis 2025年第2期59卷 1213-1237页

作者： Lu, Peipei Maier, Roland Rupp, Andreas Department of Mathematics Sciences Soochow University Suzhou215006 China Institute for Applied and Numerical Mathematics Karlsruhe Institute of Technology Englerstr. 2 Karlsruhe76131 Germany Department of Mathematics Saarland University Saarbrücken66123 Germany

We formulate and analyze a multiscale method for an elliptic problem with an oscillatory coefficient based on a skeletal (hybrid) formulation. More precisely, we employ hybrid discontinuous Galerkin approaches and combine them with the localized orthogonal decomposition methodology to obtain a coarse-scale skeletal method that effectively includes fine-scale information. This work is the first step in reliably merging hybrid skeletal formulations and localized orthogonal decomposition to unite the advantages of both strategies. numerical experiments are presented to illustrate the theoretical findings. © The authors. Published by EDP Sciences, SMAI 2025.

关键词： Geometry

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numerical Aspects of the Tensor Product Multilevel Method for High-dimensional, Kernel-based Reconstruction on Sparse Grids

arXiv

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arXiv 2025年

作者： Büttner, Markus Kempf, Rüdiger Wendland, Holger Department of Mathematics University of Bayreuth Bayreuth95440 Germany Applied and Numerical Analysis Department of Mathematics University of Bayreuth Bayreuth95440 Germany

This paper investigates the approximation of functions with finite smoothness defined on domains with a Cartesian product structure. The recently proposed tensor product multilevel method (TPML) combines Smolyak’s sparse grid method with a kernel-based residual correction technique. The contributions of this paper are twofold. First, we present two improvements on the TPML that reduce the computational cost of point evaluations compared to a naive implementation. Second, we provide numerical examples that demonstrate the effectiveness and innovation of the *** Codes 65D12, 65D15, 65D40 © 2025, CC BY.

关键词： Tensors

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Strongly coupled two-scale system with nonlinear dispersion: weak solvability and numerical simulation

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Zeitschrift fur Angewandte Mathematik und Physik 2025年第3期76卷 1-26页

作者： Raveendran, Vishnu Nepal, Surendra Lyons, Rainey Eden, Michael Muntean, Adrian Institute for Numerical Simulation University of Bonn Bonn Germany Department of Mathematics and Computer Science Karlstad University Karlstad Sweden Department of Applied Mathematics University of Colorado Boulder Boulder CO United States

We investigate a two-scale system featuring an upscaled parabolic dispersion–reaction equation intimately linked to a family of elliptic cell problems. The system is strongly coupled through a dispersion tensor, which depends on the solutions to the cell problems, and via the cell problems themselves, where the solution of the parabolic problem interacts nonlinearly with the drift term. This particular mathematical structure is motivated by a rigorously derived upscaled reaction–diffusion–convection model that describes the evolution of a population of interacting particles pushed by a large drift through an array of periodically placed obstacles (i.e., through a regular porous medium). We prove the existence and uniqueness of weak solutions to our system by means of an iterative scheme, where particular care is needed to ensure the uniform positivity of the dispersion tensor. Additionally, we use finite element-based approximations for the same iteration scheme to perform multiple simulation studies. Finally, we highlight how the choice of micro-geometry (building the regular porous medium) and of the nonlinear drift coupling affects the macroscopic dispersion of particles. © The Author(s) 2025.

关键词： Iterative scheme Nonlinear dispersion Simulation Two-scale system Weak solutions

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Towards an Adaptation of the Nonlinear Harmonics Method Realized in an Unstructured Flow Solver for Simulation of Turbomachinery Problems on Supercomputers 10th

Towards an Adaptation of the Nonlinear Harmonics Method R...

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10th Russian Supercomputing Days Conference, RuSCDays 2024

作者： Duben, Alexey Zagitov, Renat Shuvaev, Nikolay Marakueva, Olga Keldysh Institute of Applied Mathematics of Russian Academy of Sciences Moscow Russia LLC "Numerical Calculations Russia" Saint-Petersburg Russia

ISBN: (纸本)9783031784583

The nonlinear harmonics (NLH) method allows to simulate unsteady effects in turbomachines when one blade passage (periodic sector) per row is considered. numerical and computational details of the NLH realization within second-order higher accuracy control volume numerical algorithm for simulations on unstructured meshes are presented. Parallelization aspects and details of computational cost reduction in the parallel heterogeneous code NOISEtte are discussed. The performance of the NLH method is demonstrated on modeling of turbomachinery applications (single rotor Rotor67 and multi-stage compressor). The results are compared with the reference data, both experimental and numerical results obtained by a specialized software. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Mesh generation

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Local time-integration for Friedrichs’ systems

arXiv

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arXiv 2025年

作者： Hochbruck, Marlis Scheifinger, Malik Institute for Applied and Numerical Mathematics Karlsruhe Institute for Technology Karlsruhe76131 Germany

In this paper, we address the full discretization of Friedrichs’ systems with a two-field structure, such as Maxwell’s equations or the acoustic wave equation in div-grad form, cf. [14]. We focus on a discontinuous Galerkin space discretization applied to a locally refined mesh or a small region with high wave speed. This results in a stiff system of ordinary differential equations, where the stiffness is mainly caused by a small region of the spatial mesh. When using explicit time-integration schemes, the time step size is severely restricted by a few spatial elements, leading to a loss of efficiency. As a remedy, we propose and analyze a general leapfrog-based scheme which is motivated by [5]. The new, fully explicit, local time-integration method filters the stiff part of the system in such a way that its CFL condition is significantly weaker than that of the leapfrog scheme while its computational cost is only slightly larger. For this scheme, the filter function is a suitably scaled and shifted Chebyshev polynomial. While our main interest is in explicit local-time stepping schemes, the filter functions can be much more general, for instance, a certain rational function leads to the locally implicit method, proposed and analyzed in [24]. Our analysis provides sufficient conditions on the filter function to ensure full order of convergence in space and second order in time for the whole class of local time-integration *** Codes 65M12, 65M15, 65M22 Copyright © 2025, The Authors. All rights reserved.

关键词： Rational functions

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A Higher Order Unfitted Space-Time Finite Element Method for Coupled Surface-Bulk Problems

A Higher Order Unfitted Space-Time Finite Element Method for...

引用

European Conference on numerical mathematics and Advanced Applications, ENUMATH 2023

作者： Heimann, Fabian Institute for Numerical and Applied Mathematics University of Göttingen Göttingen Germany

ISBN: (纸本)9783031861727

We present a higher order space-time unfitted finite element method for convection-diffusion problems on coupled (surface and bulk) domains. In that way, we combine a method suggested by Heimann, Lehrenfeld, Preuß (SIAM J. Sci. Comput. 45(2), 2023, B139–B165) for the bulk case with a method suggested by Sass, Reusken (Comput. Math. Appl. 146(15), 2023, 253–270) for the surface case. The geometry is allowed to change with time, and the higher order discrete approximation of this geometry is ensured by a time-dependent isoparametric mapping. The space-time discretisation approach allows for straightforward handling of arbitrary high orders. In that way, we also generalise results of Hansbo, Larson, Zahedi (Comput. Methods Appl. Mech. Engrg. 307, 2016, 96–116) to higher orders. The convergence of the proposed higher order discretisations is confirmed numerically. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Finite element method

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A parallel-in-time solver for nonlinear degenerate time-periodic parabolic problems

arXiv

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arXiv 2025年

作者： Egger, Herbert Schafelner, Andreas Institute of Numerical Mathematics Johannes Kepler University Linz Austria Johann Radon Institute for Computational and Applied Mathematics Austria

A class of abstract nonlinear time-periodic evolution problems is considered which arise in electrical engineering and other scientific disciplines. An efficient solver is proposed for the systems arising after discretization in time based on a fixed-point iteration. Every step of this iteration amounts to the solution of a discretized time-periodic and time-invariant problem for which efficient parallel-in-time methods are available. Global convergence with contraction factors independent of the discretization parameters is established. Together with an appropriate initialization step, a highly efficient and reliable solver is obtained. The applicability and performance of the proposed method is illustrated by simulations of a power transformer. Further comparison is made with other solution strategies proposed in the literature. Copyright © 2025, The Authors. All rights reserved.

关键词： Iterative methods

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Application of the matrix completion algorithm for compression and data processing of sea surface temperature with sparse measurement errors

引用

Computational mathematics and Modeling 2025年 1-10页

作者： Sheloput, T.O. Petrov, S.V. Kosolapov, I.A. Institute of Numerical Mathematics of the Russian Academy of Sciences Gubkin Street 8 Moscow 119333 Russian Federation School of Applied Mathematics and Informatics MIPT Institutskiy Lane 9 Moscow Region Dolgoprudny 141701 Russian Federation

Due to the need to store and transfer an ever-increasing volume of geophysical data, the problem of developing effective compression algorithms is becoming increasingly important. In order to use geophysical data in practical applications, some preliminary processing is carried out (for example, filtration of anomalies and data interpolation). In this article, a method based on matrix approximations is applied to problems of compression, preliminary processing, and interpolation of sea surface temperature (SST). The method that we use is based on approximating the data matrix as the sum of a low-rank matrix and a sparse matrix. It is shown that it allows lossy compression of the data on sea surface temperature obtained from satellites, and it can also be used to fill in relatively small gaps in the data. The quantity of real numbers that is required to restore the approximation of the source field, depends on the permissible approximation error. In order to calculate a single element of the matrix approximation, R multiplications are required, where R denotes the rank of the matrix. The sparse component of the matrix approximation contains elements that the algorithm considers to be anomalies, and they are usually localized near the coast. A possible reason is the actual presence of anomalies in the data from coastal zones and the specifics of formation of the source matrix from the data, which may require correction. It should be noted that further numerical studies are needed to formulate recommendations for using the method for compression, processing, and data interpolation © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

关键词： Data interpolation Dea surface temperature Geophysical data compression Satellite data processing

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FINITE ELEMENT DISCRETIZATION OF NONLINEAR MODELS OF ULTRASOUND HEATING

arXiv

引用

arXiv 2025年

作者： Careaga, Julio Dörich, Benjamin Nikolić, Vanja Department of Mathematics University of Bío-Bío Chile Institute for Applied and Numerical Mathematics Karlsruhe Institute of Technology Karlsruhe76149 Germany Department of Mathematics Radboud University Heyendaalseweg 135 Nijmegen6525 AJ Netherlands

Heating generated by high-intensity focused ultrasound waves is central to many emerging medical applications, including non-invasive cancer therapy and targeted drug delivery. In this study, we aim to gain a fundamental understanding of numerical simulations in this context by analyzing conforming finite element approximations of the underlying nonlinear models that describe ultrasound-heat interactions. These models are based on a coupling of a nonlinear Westervelt–Kuznetsov acoustic wave equation to the heat equation with a pressure-dependent source term. A particular challenging feature of the system is that the acoustic medium parameters may depend on the temperature. The core of our new arguments in the a prior error analysis lies in devising energy estimates for the coupled semi-discrete system that can accommodate the nonlinearities present in the model. To derive them, we exploit the parabolic nature of the system thanks to the strong damping present in the acoustic component. Theoretically obtained optimal convergence rates in the energy norm are confirmed by the numerical experiments. In addition, we conduct a further numerical study of the problem, where we simulate the propagation of acoustic waves in liver tissue for an initially excited profile and under high-frequency *** Codes 35L05, 35L72, 34A34 Copyright © 2025, The Authors. All rights reserved.

关键词： Ultrasonic waves

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