Journal of Computational Science最新文献

This paper proposes an efficient spline-based DQ method for the 2D and 3D convection–diffusion equations (CDEs) with Riesz fractional derivative in space, which have been widely used to describe the anomalous solute transport in complex media. Firstly, a spline-based differential quadrature (DQ) formula is developed to approximate the Riesz derivative by using cubic B-splines as trial functions, which allows us to approximate the fractional derivatives with high accuracy and small computational cost. We then utilize it to discretize the fractional derivatives in the governing equation and a cubic B-spline DQ scheme is further established by applying the finite difference (FD) scheme to the resulting system of ordinary differential equations. A brief implementation of the proposed DQ method is also presented. To examine the effectiveness of this spline-based DQ method, numerical tests are finally done on some benchmark problems and the simulation of rotating Gaussian hill in convection-dominated flow governed by fractional derivatives. The advantages in computational accuracy and efficiency are illustrated by comparing the results with the other algorithms in open literature.

The Python Indian Weather Radar Toolkit, abbreviated as "pyiwr", is an open-source Python library tailored for the purpose of handling data from the Indian Doppler Weather Radar (DWR). This paper provides a comprehensive overview of the pyiwr, which serves as a toolkit to read, analyze, process, and visualize weather radar data. Apart from this, the toolkit offers a range of robust functions implementing various algorithms covering several aspects of the radar data processing and quality control that facilitate the manipulation and analysis of weather radar data. To demonstrate the practical applicability of pyiwr, various case studies are presented, focusing on processing raw reflectivity data (clutter correction), Quantitative Precipitation Estimation (QPE) using Z-R relationship and time-series analysis of reflectivity and rain intensity, both spatially as well as at a specific location, during various meteorological events. This module enhances the accessibility and compatibility of radar data, enabling researchers, weather forecasters, and hydrologists to efficiently work with DWR data (particularly Indian DWR) that fosters advancements in weather radar research and applications. The open availability of pyiwr's source code on GitHub ensures that researchers and practitioners can not only access the toolkit but also contribute to its ongoing development.

The primary objective of LIT-FED-SEARCH software is to develop a user-friendly solution tailored to researchers and scientists. This solution aims to enhance their impact by facilitating the analysis of data from modern, extensive datasets like PubMed and Clinical Trials, alongside real-world evidence. The central concept we offer is a Federated Search Workflow Engine, which has been designed and maintained to accommodate various infrastructure configurations for the convenience of users. In line with this approach, potential users have the flexibility to configure their own computing environment and a set of interesting data repositories, based on their specific requirements and capabilities. This customization can significantly reduce the time and resources invested in research. LIT-FED-SEARCH is constructed with the support of OpenSearch full-text search engine as its heart. This paper offers an overview of the system’s architecture, capabilities, and potential applications in the field of biomedical research.

Partial differential equations (PDEs) are widely used to describe relevant phenomena in dynamical systems. In real-world applications, we commonly need to combine formal PDE models with (potentially noisy) observations. This is especially relevant in settings where we lack information about boundary or initial conditions, or where we need to identify unknown model parameters. In recent years, Physics-Informed Neural Networks (PINNs) have become a popular tool for this kind of problems. In high-dimensional settings, however, PINNs often suffer from computational problems because they usually require dense collocation points over the entire computational domain. To address this problem, we present Physics-Informed Boundary Integral Networks (PIBI-Nets) as a data-driven approach for solving PDEs in one dimension less than the original problem space. PIBI-Nets only require points at the computational domain boundary, while still achieving highly accurate results. Moreover, PIBI-Nets clearly outperform PINNs in several practical settings. Exploiting elementary properties of fundamental solutions of linear differential operators, we present a principled and simple way to handle point sources in inverse problems. We demonstrate the excellent performance of PIBI-Nets for the Laplace and Poisson equations, both on artificial datasets and within a real-world application concerning the reconstruction of groundwater flows.

The present study assesses RANS-based turbulence models to simulate the isothermal confined swirling flow in a combustor representing a constituent can combustor of the can-annular configuration used in jet engines. The two-equation models (standard $k-ϵ$, realizable $k-ϵ$, standard $k-\omega$, SST $k-\omega$), and seven-equation model (linear pressure strain-Reynolds stress model, LPS-RSM), are assessed by comparing their predictions of mean axial velocity, mean transverse velocity, turbulent kinetic energy, and shear stress with the experimental data at two different positions (i.e., the primary and dilution hole planes) in the combustor. While the two-equation models generally have failed to predict the confined swirling flow at both positions accurately, the SST $k-\omega$ model yielded the most accurate, followed by standard $k-\omega$ and realizable $k-ϵ$ models. The discrepancies between the computational and experimental results could be attributed to the isotropic turbulence assumptions, which, however, are invalid for confined swirling flows. Further, the two-equation model formulations cannot capture the intricacies of vortex flow and its interaction with the surroundings in confined swirling flows. The LPS-RSM, which considers turbulence anisotropy, showed some promise, although overpredicted results follow the trend with experimental values at the primary holes plane. However, at the dilution holes plane, the model overpredicted the velocity field, and underestimated the turbulence field, including turbulent kinetic energy and shear stress. These observed discrepancies can be ascribed to the pressure-strain correlation in the LPS-RSM, which assumes the pressure is a linear function of the strain-rate tensor. However, this linear assumption is quite simplistic for complex flows. Further, the influence of discretization (SOU and third-order MUSCL) schemes of convective terms is also assessed, and the differences in predictions resulted from MUSCL scheme having lower diffusion and superior ability to capture sharper gradients, however, did not translate into improving the solution accuracy. Hence, this study suggests that more advanced high-fidelity turbulence models (e.g., hybrid RANS-LES, LES, DNS) are needed to accurately predict the confined swirling flow in combustors.

In atomistic spin dynamics simulations, the time cost of constructing the space- and time-displaced pair correlation function in real space increases quadratically as the number of spins $N$, leading to significant computational effort. The GEMM subroutine can be adopted to accelerate the calculation of the dynamical spin–spin correlation function, but the computational cost of simulating large spin systems ($>40000$ spins) on CPUs remains expensive. In this work, we perform the simulation on a graphics processing unit (GPU), a hardware solution widely used as an accelerator for scientific computing and deep learning. We show that GPUs can accelerate the simulation up to 25-fold compared to multi-core CPUs when using the GEMM subroutine on both. To hide memory latency, we fuse the element-wise operation into the GEMM kernel using $CUTLASS$ which can improve the performance by 26% $\sim$ 33% compared to the implementation based on $cuBLAS$. Furthermore, we perform the ‘on-the-fly’ calculation in the epilogue of the GEMM subroutine to avoid saving intermediate results on global memory, which makes large-scale atomistic spin dynamics simulations feasible and affordable.

We present a comparison of Physics Informed Neural Networks (PINN) and Variational Physics Informed Neural Networks (VPINN) with higher-order and continuity Finite Element Method (FEM). We focus on the one-dimensional advection-dominated diffusion problem and the two-dimensional Eriksson–Johnson model problem. We show that the standard Galerkin method for FEM cannot solve this problem on uniform grid. We discuss the stabilization of the advection-dominated diffusion problem with the Petrov–Galerkin (PG) formulation and present the FEM solution obtained with the PG method. The main benefit of using a stabilization method is that it can deliver a good-quality approximation to the solution on a mesh that is not fully refined towards the singularity. We employ PINN and VPINN methods, defining several strong and weak loss functions. We compare the training and solutions of PINN and VPINN methods with higher-order FEM methods. We consider a case with uniform FEM and uniform distribution of points for PINN, as well as uniform distribution of test functions for VPINN. We also consider adaptive FEM, refined towards edge singularity, and non-uniform distribution of points for PINN, as well as non-uniform distribution of test functions for VPINN.

The human brain is an enormous scientific challenge. Knowledge of the complete map of neuronal connections (connectome) is essential for understanding how neuronal circuits encode information and the brain works in health and disease. Nanoscale connectomes are created for a few small animals but not yet for the human. The key challenges in the development of a whole human brain model at the nanoscale are data acquisition and computing including big data and high performance computing. This work focuses on big data and volumetric and geometric modeling of brain morphology at the micro- and nanoscales. It presents the volumetric and four geometric neuronal models and estimates the storage required for them. It introduces four geometric neuronal models: straight wireframe, enhanced wireframe, straight polygonal, and enhanced polygonal. The volumetric model requires approximately from 4.2 to 33.6 petabytes (PB) at the microscale up to 5,600,000 exabytes (EB) at the nanoscale. The straight wireframe model requires 18 PB at the microscale and 24 PB at the nanoscale. The enhanced parabolic wireframe model needs 36 PB at the microscale and 48 PB at the nanoscale, whereas the enhanced cubic model requires 54 PB at the microscale and 72 PB at the nanoscale. The straight polygonal model requires 24 PB at the microscale and 32 PB at the nanoscale. The enhanced parabolic polygonal model needs 48 PB at the microscale and 64 PB at the nanoscale, while the enhanced cubic model needs 72 PB at the microscale and 96 PB at the nanoscale. The straight wireframe model of 18 PB is sufficient to enable computing of the human synaptome and subsequently the connectome. The only operational supercomputer able to provide such storage is the world’s first exascale supercomputer Frontier. The sizes of the volumetric and geometric models are comparable at the microscale, however, their difference is dramatic at the nanoscale; for the 10 nm resolution the geometric models are smaller approximately from 58 to 233 thousand times, and for the 1 nm resolution from 58 to 233 million times. This novel work is an extended version of a conference paper [15] and it represents a step forward toward the development of the human whole brain model at the nanoscale.

Mérope is a software devoted to the geometrical design and the discretization of microstructures of random heterogeneous materials. Mérope aims at building large samples of microstructured materials, called Representative Volume Elements, in order to derive their effective physical behaviors. Various microstructures are supported: spherical, polyhedral or spheropolyhedral inclusions, polycrystals, Gaussian fields and Boolean combinations of these. Discretization takes two forms: either regular Cartesian grids of (composite) voxels for computations with FFT-based solvers, or tetrahedral meshes for computations with Finite Element solvers. A special emphasis on the code has been put on performance, which will be further improved in the future.

This article aims at introducing the main features of the software as well as exemplifying its use.

Phenomena in life sciences can be modeled using systems of reaction–diffusion partial differential equations with cross-diffusion. These equations, nonlinear in nature, exhibit complex spatial behavior. Within this framework, we propose an SIR model with cross-diffusion to depict the dynamic interaction between susceptible and infectious individuals in the presence of public policies. Achieving accurate solutions requires fine space discretization, leading to high computational costs. In addition, we propose a second-order semi-implicit method based on an Alternating Direction Implicit (ADI) scheme, called SSI${}_{ADI}$, suitable for treating nonlinear reaction and linear diffusion problems.