Article
Computer Science, Interdisciplinary Applications
Shantanu Shahane, Anand Radhakrishnan, Surya Pratap Vanka
Summary: Meshless solution using radial basis functions (RBF) is an alternative to grid based methods, eliminating issues like grid skewness. By employing Polyharmonic splines (PHS), rapid convergence and solution to incompressible Navier-Stokes equations can be achieved.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
J. Antoon van Hooft, Stephane Popinet
Summary: This article presents a numerical solver for the incompressible Navier-Stokes equations. The solver combines fourth-order-accurate discrete approximations and an adaptive tree grid to achieve high accuracy and efficiency. The solver employs a novel compact-upwind advection scheme and a 4th-order accurate projection algorithm to satisfy the incompressibility constraint. The paper also introduces a new refinement indicator tailored to this solver and demonstrates the consistency and convergence rate of the adaptive solver through tests and examples.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Eduardo Jourdan, Z. J. Wang
Summary: This article addresses two acceleration techniques, p-multigrid and local Mach number preconditioning, in the context of high-order methods. The use of Mach number preconditioning significantly enhances the efficiency of the p-multigrid method, especially for unsteady simulations with larger physical time steps.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2022)
Article
Multidisciplinary Sciences
Teeratorn Kadeethum, Daniel O'Malley, Francesco Ballarin, Ida Ang, Jan N. Fuhg, Nikolaos Bouklas, Vinicius L. S. Silva, Pablo Salinas, Claire E. Heaney, Christopher C. Pain, Sanghyun Lee, Hari S. Viswanathan, Hongkyu Yoon
Summary: In this study, a novel approach using reduced order modeling (ROM) is proposed to reduce computational cost and improve convergence rate of nonlinear solvers for solving partial differential equations. By utilizing ROM's prediction as an initial guess, the computational efficiency of the solvers can be enhanced, leading to improved convergence of the solutions.
SCIENTIFIC REPORTS
(2022)
Article
Mathematics, Applied
Syed Ahmed Pasha, Yasir Nawaz, Muhammad Shoaib Arif
Summary: This paper presents a method that guarantees third-order temporal accuracy in solving time-dependent parabolic and first-order hyperbolic partial differential equations (PDEs). Stability conditions are derived using Von Neumann stability analysis to ensure convergence of the algorithm. The performance of the algorithm is demonstrated for linear and nonlinear parabolic PDEs with viscous dissipation and thermal radiation effects.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Computer Science, Interdisciplinary Applications
P. C. Africa, M. Salvador, P. Gervasio, L. Dede', A. Quarteroni
Summary: This paper proposes a matrix-free solver based on the spectral element method for numerically solving the cardiac electrophysiology model. It combines vectorization with sum-factorization to achieve efficient high-performance computing using high-order polynomials. The effectiveness and efficiency of the solver are validated and demonstrated through various applications and electrophysiological simulations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Pierre-Loic Bacq, Yvan Notay
Summary: This article presents a numerical method for solving discrete Oseen problems. The method involves an algebraic transformation and aggregation-based algebraic two-grid preconditioning. An algebraic analysis is provided, showing that the method has uniform convergence with respect to problem parameters. Further analysis reveals that the method can handle constant convection fields if the pressure unknowns are coarsened based on the convection field. The method is distinct from a similar method for Stokes equations and requires either point-based coarsening or construction of an auxiliary convection-diffusion matrix to guide the coarsening. Promising results are obtained, demonstrating that the number of iterations is uniformly bounded with respect to mesh size and Reynolds number even in challenging situations.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2023)
Article
Computer Science, Interdisciplinary Applications
E. Ferrer, G. Rubio, G. Ntoukas, W. Laskowski, O. A. Marino, S. Colombo, A. Mateo-Gabin, H. Marbona, F. Manrique de Lara, D. Huergo, J. Manzanero, A. M. Rueda-Ramirez, D. A. Kopriva, E. Valero
Summary: We present the latest developments of our open source high-order discontinuous Galerkin framework, capable of solving a variety of flow applications. The solver is parallelised and shows good scalability. Temporal discretisations include explicit, implicit, multigrid, and dual time-stepping schemes. Additionally, we facilitate meshing and simulating complex geometries through a mesh-free immersed boundary technique.
COMPUTER PHYSICS COMMUNICATIONS
(2023)
Article
Astronomy & Astrophysics
Richard E. L. Higgins, David F. Fouhey, Dichang Zhang, Spiro K. Antiochos, Graham Barnes, J. Todd Hoeksema, K. D. Leka, Yang Liu, Peter W. Schuck, Tamas I. Gombosi
Summary: This paper introduces a deep-learning-based approach that can simulate the existing HMI pipeline results two orders of magnitude faster than current algorithms.
ASTROPHYSICAL JOURNAL
(2021)
Article
Computer Science, Software Engineering
Sadiq H. Abdulhussain, Basheera M. Mahmmod, Thar Baker, Dhiya Al-Jumeily
Summary: This article introduces a computationally efficient and numerically stable algorithm for generating discrete Tchebichef polynomials (DTPs) coefficients, which can be applied to high order moments and large signal sizes.
CONCURRENCY AND COMPUTATION-PRACTICE & EXPERIENCE
(2022)
Article
Engineering, Multidisciplinary
Zisheng Ye, Xiaozhe Hu, Wenxiao Pan
Summary: This paper presents a monolithic geometric multigrid preconditioner for solving fluid-solid interaction problems in the Stokes limit. The preconditioner is constructed using the generalized moving least squares (GMLS) method with adaptive h-refinement. Numerical examples demonstrate that the proposed preconditioner ensures convergence and good scalability as the total degrees of freedom and the number of solid bodies increase.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mathematics, Applied
Matthias Bolten, Marco Donatelli, Paola Ferrari, Isabella Furci
Summary: The main focus of this paper is the study of efficient multigrid methods for large linear systems with a particular saddle-point structure. The paper proposes a symbol based convergence analysis for problems that have a hidden block Toeplitz structure and provides optimal parameters for the preconditioning of the saddle-point problem. The efficiency and convergence rate of the proposed methods are demonstrated through numerical tests.
APPLIED NUMERICAL MATHEMATICS
(2023)
Article
Water Resources
Nickolay M. Evstigneev, Oleg I. Ryabkov, Kirill M. Gerke
Summary: This paper presents a high efficiency Stokes solver for incompressible flow in porous media. The solver utilizes a fast algebraic multigrid method on graphics processing units (GPUs) to reduce memory usage and accelerate computation. A simple MAC-type staggered finite difference discretization is used, and a coupled Stokes saddle-point type system is directly solved on a GPU. The method includes topological domain analysis on a GPU to remove isolated volumes with no flow. Various types of boundary conditions and efficient parallel strategies for GPUs are considered. The method is extensively benchmarked against analytical solutions and applied problems from digital rock physics. The results demonstrate the effectiveness and efficiency of the proposed method.
ADVANCES IN WATER RESOURCES
(2023)
Article
Optics
Wei Liu, Jiawen Liao, Yu Yu, Xinliang Zhang
Summary: The proposed integrated division-of-time polarimeter (DOTP) improves measuring efficiency and accuracy by simultaneously measuring a pair of orthogonal polarization states. Optimization of the analysis matrix reduces the influence of photodetector noise, leading to improved performance compared to conventional designs.
Article
Computer Science, Interdisciplinary Applications
Ki-Tae Kim, Klaus-Jurgen Bathe
Summary: The paper presents a solution scheme for accurate wave propagation in general solids, based on overlapping finite elements and direct time integration. The scheme effectively reduces spatial and time integration errors, leading to a monotonic reduction in total dispersion error when simulating multiple waves traveling through solids.
COMPUTERS & STRUCTURES
(2021)
