Computer Physics Communications最新文献

{"title":"A comparison of Bayesian sampling algorithms for high-dimensional particle physics and cosmology applications","authors":"The DarkMachines High Dimensional Sampling Group,&nbsp;Joshua Albert ,&nbsp;Csaba Balázs ,&nbsp;Andrew Fowlie ,&nbsp;Will Handley ,&nbsp;Nicholas Hunt-Smith ,&nbsp;Roberto Ruiz de Austri ,&nbsp;Martin White","doi":"10.1016/j.cpc.2025.109756","DOIUrl":"10.1016/j.cpc.2025.109756","url":null,"abstract":"<div><div>For several decades now, Bayesian inference techniques have been applied to theories of particle physics, cosmology and astrophysics to obtain the probability density functions of their free parameters. In this study, we review and compare a wide range of Markov chain Monte Carlo (MCMC) and nested sampling techniques to determine their relative efficacy on functions that resemble those encountered most frequently in the particle astrophysics literature. Our first series of tests explores a series of high-dimensional analytic test functions that exemplify particular challenges, for example highly multimodal posteriors or posteriors with curving degeneracies. We then investigate two real physics examples, the first being a global fit of the Λ CDM model using cosmic microwave background data from the Planck experiment, and the second being a global fit of the Minimal Supersymmetric Standard Model using a wide variety of collider and astrophysics data. We show that several examples widely thought to be most easily solved using nested sampling approaches can in fact be more efficiently solved using modern MCMC algorithms, but the details of the implementation matter. Furthermore, we also provide a series of useful insights for practitioners of particle astrophysics and cosmology.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"315 ","pages":"Article 109756"},"PeriodicalIF":7.2,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144694590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Flowy: High performance probabilistic lava emplacement prediction","authors":"Moritz Sallermann ,&nbsp;Amrita Goswami ,&nbsp;Alejandro Peña-Torres ,&nbsp;Rohit Goswami","doi":"10.1016/j.cpc.2025.109745","DOIUrl":"10.1016/j.cpc.2025.109745","url":null,"abstract":"<div><div>Lava emplacement is a complex physical phenomenon, affected by several factors. These include, but are not limited to features of the terrain, the lava settling process, the effusion rate or total erupted volume, and the probability of effusion from different locations. One method, which has been successfully employed to predict lava flow emplacement and forecast the inundated area and final lava thickness, is the MrLavaLoba method from Vitturi et al. <span><span>[1]</span></span>. The MrLavaLoba method has been implemented in their code of the same name <span><span>[2]</span></span>. Here, we introduce Flowy, a new computational tool that implements the MrLavaLoba method in a more efficient manner. New fast algorithms have been incorporated for all performance critical code paths, resulting in a complete overhaul of the implementation. When compared to the MrLavaLoba code <span><span>[1]</span></span>, <span><span>[2]</span></span>, Flowy exhibits a significant reduction in runtime – between 100 to 400 times faster – depending on the specific input parameters. The accuracy and the probabilistic convergence of the model outputs are not compromised, maintaining high fidelity in generating possible lava flow paths and deposition characteristics. We have validated Flowy's performance and reliability through comprehensive unit-testing and a real-world eruption scenario. The source code is freely available on GitHub <span><span>[3]</span></span>, facilitating transparency, reproducibility and collaboration within the geoscientific community.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"315 ","pages":"Article 109745"},"PeriodicalIF":7.2,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655008","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Simplified coupled atmosphere-fire model for simulation of 2D wildland fires","authors":"Daniel San Martin ,&nbsp;Claudio E. Torres","doi":"10.1016/j.cpc.2025.109746","DOIUrl":"10.1016/j.cpc.2025.109746","url":null,"abstract":"<div><div>Every year, wildfires pose a significant problem worldwide, particularly during the summer season. Many computational models have been developed to simulate and study the effects of fire dynamics. This work proposes a coupled but simplified atmosphere-fire model to describe the phenomena in a step further than uncoupled fire spread models while avoiding the high computational cost of large coupled models. This article presents the formalization of the model and the numerical methods employed to approximate its numerical solution. Despite the simplifications and assumptions made, the model achieves competitive results in terms of capturing the fire spreading behavior and computational requirements thanks to strategies such as a two-dimensional spatial domain, turbulence modeling, topography handling by the Immersed Boundary Method, and mixed Finite Difference with Discrete Fourier Transform for the pressure solver. The proposed model and its numerical implementation are the first step towards an extended version with a three-dimensional spatial domain.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"315 ","pages":"Article 109746"},"PeriodicalIF":7.2,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144657200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A distributed-memory tridiagonal solver based on a specialised data structure optimised for CPU and GPU architectures","authors":"Semih Akkurt ,&nbsp;Sébastien Lemaire ,&nbsp;Paul Bartholomew ,&nbsp;Sylvain Laizet","doi":"10.1016/j.cpc.2025.109747","DOIUrl":"10.1016/j.cpc.2025.109747","url":null,"abstract":"<div><div>Various numerical methods used for solving partial differential equations (PDE) result in tridiagonal systems. Solving tridiagonal systems on distributed-memory environments is not straightforward, and often requires significant amount of communication. In this article, we present a novel distributed-memory tridiagonal solver algorithm, DistD2-TDS, based on a specialised data structure. DistD2-TDS algorithm takes advantage of the diagonal dominance in tridiagonal systems to reduce the communications in distributed-memory environments based on an established strategy. The underlying data structure plays a crucial role for the performance of the algorithm on individual ranks. First, the data structure improves data localities and makes it possible to minimise data movements via cache blocking and kernel fusion strategies. Second, data continuity enables a contiguous data access pattern and results in efficient utilisation of the available memory bandwidth. Finally, the data layout supports vectorisation on CPUs and thread level parallelisation on GPUs for improved performance. In order to demonstrate the robustness of the algorithm, we implemented and benchmarked the algorithm on CPUs and GPUs. We investigated the single rank performance and compared against existing algorithms. Furthermore, we analysed the strong scaling of the implementation up to 384 NVIDIA H100 GPUs and up to 8192 AMD EPYC 7742 CPUs. Finally, we demonstrated a practical use case of the algorithm by using compact finite difference schemes to solve a 3D non-linear PDE. The results demonstrate that DistD2 algorithm can sustain around 66% of the theoretical peak bandwidth at scale on CPU and GPU based supercomputers.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"315 ","pages":"Article 109747"},"PeriodicalIF":7.2,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Incremental pressure correction method for high-performance simulations of subsonic compressible flows","authors":"Jérôme Jansen ,&nbsp;Stéphane Glockner ,&nbsp;Deewakar Sharma ,&nbsp;Arnaud Erriguible","doi":"10.1016/j.cpc.2025.109742","DOIUrl":"10.1016/j.cpc.2025.109742","url":null,"abstract":"<div><div>In the present work, we propose a time-splitting method to handle the treatment of pressure-velocity coupling in the context of subsonic compressible flows. We extend the well-known <em>incremental pressure correction method for incompressible flows</em> to subsonic compressible flows by solving, at each time step and for the temporal pressure increment variable, an elliptic equation involving a linear term. The governing equations, written in primitive variables, consist of the compressible Navier–Stokes equations along with the energy conservation equation. Closure with any chosen fluid equation of state enables the calculation of relevant thermophysical fluid properties. After deriving the proposed method and recalling its <em>non-incremental</em> counterpart, spatial and temporal second-order convergence are measured for both methods on various verification test cases. The classical pressure accuracy limitations of the <em>non-incremental</em> method for incompressible flows are overcome when applied to compressible subsonic flows due to the different nature of the pressure equation. The <em>incremental</em> method is subsequently applied to steady and unsteady high-gradient temperature and density flows, <em>i.e.</em> beyond the Boussinesq approximation known as Non-Oberbeck-Boussinesq flows, such as thermoacoustic wave propagation and natural convection problems. Both verification and validation processes are systematically and carefully detailed. Finally, Direct Numerical Simulation of three-dimensional compressible Rayleigh–Bénard turbulent convection of highly compressible fluid supercritical carbon dioxide is proposed. The parallel implementation efficiency of the method is also reported throught strong and weak scalability tests in the last three-dimensional case up to 131,072 cores. We demonstrate the capacity to provide a full second-order accurate and efficient incremental pressure correction method to solve subsonic compressible flows.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"315 ","pages":"Article 109742"},"PeriodicalIF":7.2,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632680","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A local and explicit forcing correction for Lagrangian immersed boundary methods","authors":"Giovanni Vagnoli ,&nbsp;Martino Andrea Scarpolini ,&nbsp;Roberto Verzicco ,&nbsp;Francesco Viola","doi":"10.1016/j.cpc.2025.109741","DOIUrl":"10.1016/j.cpc.2025.109741","url":null,"abstract":"<div><div>Lagrangian immersed boundary methods (IBM) are widely used to study flows with complex and moving boundaries, such as biological flows. However, it has been noted that in some cases the resulting no-slip condition at the wet tissues is inaccurate. In this work, we propose an improved technique to evaluate the IBM forces with the aim of reducing slip and transpiration velocities at the immersed wet surfaces. In the framework of Moving Least Squares transfer function (MLS-IBM), we first formulate the problem of determining the IB forces in an implicit manner. Although this approach enforces the no-slip condition to machine precision, we demonstrate that this method is unaffordable for moderate/high Reynolds number flows. Nevertheless, insight of the implicit formulation reveals that it is possible to derive analytically a local correction to the IB forcing via an approximate factorisation of the system matrix of the implicit IBM. The resulting correction is fully explicit and it can be easily implemented in existing IB codes and extended to other Lagrangian IBMs. Our approach is then tested and compared against standard IBM-MLS (also in its iterative version) in a series of benchmark flows, including fixed and moving rigid bodies, and finally in the biological flow within a rigid aorta. Importantly, the proposed correction is seen to greatly improve the consistency and convergence properties of the IBM-MLS.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"315 ","pages":"Article 109741"},"PeriodicalIF":7.2,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Perfectly Matched Layers implementation for E-H fields and complex wave envelope propagation in the Smilei PIC code","authors":"Guillaume Bouchard ,&nbsp;Arnaud Beck ,&nbsp;Francesco Massimo ,&nbsp;Arnd Specka","doi":"10.1016/j.cpc.2025.109737","DOIUrl":"10.1016/j.cpc.2025.109737","url":null,"abstract":"<div><div>The design of absorbing boundary conditions (ABC) in a numerical simulation is a challenging task. In the best cases, spurious reflections remain for some angles of incidence or at certain wavelengths. In the worst, ABC are not even possible for the set of equations and/or numerical schemes used in the simulation and reflections can not be avoided at all. Perfectly Matched Layers (PML) are layers of absorbing medium which can be added at the simulation edges in order to significantly damp both outgoing and reflected waves, thus effectively playing the role of an ABC. They are able to absorb waves and prevent reflections for all angles and frequencies at a modest computational cost. They increase the simulation accuracy and negate the need of oversizing the simulation usually imposed by ABC which normally leads to a waste of computational resources and power. In this paper, a uniform derivation of PML for finite-difference time-domain (FDTD) schemes and various geometries in Particle-In-Cell (PIC) codes is presented for Maxwell's equations and, for the first time, extended to the full envelope wave equation. An implementation of these methods in the open source PIC code <span>Smilei</span> is proposed and benchmarked.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"315 ","pages":"Article 109737"},"PeriodicalIF":7.2,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144657202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"ANEMONE: A framework for three-dimensional simulations of solid-state electroaerodynamic propulsion systems","authors":"Hisaichi Shibata ,&nbsp;Soya Shimizu ,&nbsp;Takahiro Nozaki","doi":"10.1016/j.cpc.2025.109749","DOIUrl":"10.1016/j.cpc.2025.109749","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Solid-state electro-aerodynamic propulsion systems are devices that utilize atmospheric pressure corona discharge and have been actively researched in recent years as a means of achieving silent drones. However, these systems contain multiple, widely disparate time and spatial scales. Therefore, the governing equations of the systems, a three-component plasma fluid model that considers the presence of electrons, positive ions, and negative ions, constitute a stiff non-linear system of partial differential equations, challenging to solve. Here, we have developed an ANEMONE simulator capable of numerically estimating the corona inception voltage and energy conversion efficiency in three-dimensional solid-state electro-aerodynamic propulsion systems. Specifically, on the basis of the governing equations, we adopted the method of characteristics and the perturbation method to obtain the sub-problems. Furthermore, we have successfully obtained the integral equations, making the sub-problems easier to solve. Finally, we validated the prediction results based on the theoretical results in a previous study. Remarkably, ANEMONE is the first simulator in the world which predicted the two representative performance (i.e., the corona inception voltage and energy conversion efficiency) of fully three-dimensional propulsion systems.&lt;/div&gt;&lt;/div&gt;&lt;div&gt;&lt;h3&gt;Program summary&lt;/h3&gt;&lt;div&gt;&lt;em&gt;Program Title:&lt;/em&gt; ANEMONE&lt;/div&gt;&lt;div&gt;&lt;em&gt;CPC Library link to program files:&lt;/em&gt; &lt;span&gt;&lt;span&gt;&lt;span&gt;https://doi.org/10.17632/2sxsg2pmyp.1&lt;/span&gt;&lt;/span&gt;&lt;svg&gt;&lt;path&gt;&lt;/path&gt;&lt;/svg&gt;&lt;/span&gt;&lt;/div&gt;&lt;div&gt;&lt;em&gt;Licensing provisions:&lt;/em&gt; MIT&lt;/div&gt;&lt;div&gt;&lt;em&gt;Programming language:&lt;/em&gt; C++&lt;/div&gt;&lt;div&gt;&lt;em&gt;Nature of problem:&lt;/em&gt; Solid-state electro-aerodynamic propulsion system [1] ionizes the ambient air and can propel silent drones. For the rapid-prototyping of the system, it is important to utilize numerical simulation, but the spatial and temporal scales of the system are diverse; hence, the corresponding governing equations (e.g. the three-component plasma fluid model which can simultaneously consider electrons, positive and negative ions) are too stiff to solve. For example, the overall spatial scale of the system is the order of meters, while the scale of the electrodes is the order of micrometers. Moreover, the ions move between electrodes in the order of milliseconds, while the Maxwell dielectric relaxation time scale is in the order of nanoseconds.&lt;/div&gt;&lt;div&gt;&lt;em&gt;Solution method:&lt;/em&gt; For the issue of the spatial scales, we adopt a three-dimensional hierarchical Cartesian grid method together with the adaptive mesh refinement method. Moreover, this leads fully automatic mesh generation and ensures the grid convergence. For the issue of the temporal scales, we adopt the perturbation method [2] combined with the method of characteristics. This can decompose the original problem into many subproblems easy to solve.&lt;/div&gt;&lt;/div&gt;&lt;div&gt;&lt;h3&gt;References&lt;/h3&gt;&lt;div&gt;&lt;ul&gt;&lt;li&gt;&lt;span&gt;[1]&lt;/span&gt;&lt;span&gt;&lt;di","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"315 ","pages":"Article 109749"},"PeriodicalIF":7.2,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144597092","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Q-POP-IMT: An open-source phase-field software for simulating insulator-metal transition processes in quantum materials","authors":"Yin Shi ,&nbsp;Xiaofeng Xu ,&nbsp;Xiaoxing Cheng ,&nbsp;Saurav Shenoy ,&nbsp;Jinchao Xu ,&nbsp;Long-Qing Chen","doi":"10.1016/j.cpc.2025.109751","DOIUrl":"10.1016/j.cpc.2025.109751","url":null,"abstract":"<div><div>Insulator-metal transitions in quantum materials have important potential applications in areas such as field-effect transistors and neuromorphic computing. Here we present an initial release of the Q-POP-IMT module, an open-source phase-field software for simulating mesoscopic, nonequilibrium processes of insulator-metal transitions in quantum materials. Q-POP-IMT solves the phase-field equations of evolution that describe insulator-metal transitions at the mesoscale using the finite element method. It currently utilizes the powerful FEniCS library to define and solve finite element problems. Thanks to the finite element method, the code can address general boundary conditions such as a complex integral boundary condition corresponding to one of the most common setups in experiments and applications. We demonstrate the usage of the code through simulating the neuron-like voltage self-oscillation phenomenon in a prototypical correlated material, vanadium dioxide.</div></div><div><h3>Program summary</h3><div><em>Program Title:</em> Quantum Phase-field Open-source Package - Insulator-Metal Transitions (Q-POP-IMT)</div><div><em>CPC Library link to program files:</em> <span><span>https://doi.org/10.17632/p3395559s6.1</span><svg><path></path></svg></span></div><div><em>Developer's repository link:</em> <span><span>https://github.com/DOE-COMMS/Q-POP-Modules</span><svg><path></path></svg></span></div><div><em>Licensing provisions:</em> MIT</div><div><em>Programming language:</em> Python</div><div><em>Nature of problem:</em> Correlated quantum materials often exhibit insulator-metal transitions at high temperatures, which have fascinating applications in neuromorphic computing, field-effect transistors, etc. Understanding insulator-metal transitions and designing their applications require the knowledge of the mesoscopic, nonequilibrium, inhomogeneous processes of such electronic phase transitions.</div><div><em>Solution method:</em> Q-POP-IMT code implements the phase-field equations of insulator-metal transitions in quantum materials, which describe the mesoscopic, nonequilibrium, inhomogeneous dynamics of such phase transitions. It uses the finite element method to solve the coupled nonlinear partial differential equations.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"315 ","pages":"Article 109751"},"PeriodicalIF":7.2,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144597091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A non-periodic particle mesh Ewald method for radially symmetric kernels in free space","authors":"Dennis M. Elking","doi":"10.1016/j.cpc.2025.109739","DOIUrl":"10.1016/j.cpc.2025.109739","url":null,"abstract":"&lt;div&gt;&lt;div&gt;The FFT-based smooth particle mesh Ewald (PME) method is extended to non-periodic charge systems interacting via a radially symmetric kernel &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. The proposed non-periodic PME (NPME) method begins by splitting the kernel &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; into a short-range component &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and a smooth long-range component &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. A Fourier extension for &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is computed numerically using discrete Fourier transform interpolation, enabling efficient treatment of anisotropic rectangular charge volume and offering additional flexibility in the choice of kernel splitting. A derivative-matched (DM) splitting is introduced for general radially symmetric kernels &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, improving computational performance over traditional Ewald splitting methods. An optimized grid storage algorithm for NPME is proposed, reducing total grid memory by a factor of four. The NPME algorithm is implemented in a C++ library, &lt;span&gt;npme&lt;/span&gt;, which supports both pre-defined kernels (e.g. &lt;span&gt;&lt;math&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;exp&lt;/mi&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;) and user-defined kernels via C++ classes. &lt;span&gt;npme&lt;/span&gt; is benchmarked and compared to &lt;span&gt;fmm3D&lt;/span&gt; on test systems in computational chemistry and computational electromagnetics. As a practical application, NPME is combined with Method of Moments (MoM) to form a hybrid MoM-NPME algorithm for calculating the radar cross section (RCS) of a perfect electric conductor (PEC). The MoM–NPME method is used to compute the bistatic RCS of a 1-meter PEC sphere at 37.8 GHz and the monostatic RCS of the NASA almond at 75 GHz.&lt;/div&gt;&lt;/div&gt;&lt;div&gt;&lt;h3&gt;Program summary&lt;/h3&gt;&lt;div&gt;&lt;em&gt;Program Title:&lt;/em&gt; &lt;span&gt;npme&lt;/span&gt;&lt;/div&gt;&lt;div&gt;&lt;em&gt;CPC Library link to program files:&lt;/em&gt; &lt;span&gt;&lt;span&gt;&lt;span&gt;https://doi.org/10.17632/vs86pk3dpt.1&lt;/span&gt;&lt;/span&gt;&lt;svg&gt;&lt;path&gt;&lt;/path&gt;&lt;/svg&gt;&lt;/span&gt;&lt;/div&gt;&lt;div&gt;&lt;em&gt;Developer's repository link:&lt;/em&gt; &lt;span&gt;&lt;span&gt;&lt;span&gt;https://github.com/ElkingD/npme&lt;/span&gt;&lt;/span&gt;&lt;svg&gt;&lt;path&gt;&lt;/path&gt;&lt;/svg&gt;&lt;/span&gt;&lt;/div&gt;&lt;div&gt;&lt;em&gt;Licensing provisions:&lt;/em&gt; Apache 2.0&lt;/div&gt;&lt;div&gt;&lt;em&gt;Programming language:&lt;/em&gt; C++&lt;/div&gt;&lt;div&gt;&lt;em&gt;Supplementary material:&lt;/em&gt; A supplementary material containing additional technical details and results is provided.&lt;/div&gt;&lt;div&gt;&lt;em&gt;Nature of problem:&lt;/em&gt; &lt;span&gt;npme&lt;/span&gt; computes the potential and its gradient of &lt;em&gt;N&lt;/em&gt; ","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"315 ","pages":"Article 109739"},"PeriodicalIF":7.2,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144597089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}