Article
Computer Science, Interdisciplinary Applications
J. Blair Perot, Chris Chartrand
Summary: This paper introduces a new method for mimetic interpolation on polygonal meshes based on harmonic function interpolation. It highlights the use of truncated harmonic polynomial expansions for computational efficiency and demonstrates the stability and accuracy of higher level truncations of harmonic interpolations. The versatility and accuracy of this numerical method is showcased in a multiphase incompressible flow problem with a density jump of 1000 on a moving polygonal mesh.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
M. H. Heydari, M. Hosseininia, D. Baleanu
Summary: In this paper, a numerical method based on orthonormal shifted discrete Chebyshev polynomials is proposed to solve the complex solution of the Helmholtz equation. This method transforms the equation into an algebraic system of equations that can be easily solved. Four practical examples are provided to demonstrate the accuracy of the proposed technique.
Article
Mathematics, Applied
Andrew Gibbs, Simon N. Chandler-Wilde, Stephen Langdon, Andrea Moiola
Summary: We propose a boundary element method for time-harmonic acoustic scattering by multiple obstacles in two dimensions, where at least one of the obstacles is a convex polygon. By combining a hybrid numerical-asymptotic approximation space with standard polynomial-based approximation spaces, the method reduces the number of degrees of freedom required in the HNA space to grow logarithmically with respect to frequency. This method is most effective when the convex polygon is large in diameter and the combined perimeter of the small obstacles is comparable to the wavelength of the problem.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2021)
Article
Nuclear Science & Technology
Xinyu Wang, Bin Zhang, Ni Dai, Yixue Chen
Summary: The multicollision sources (MCS) algorithm reduces discretization errors by spatial decomposition and considering the distribution of flux in different regions and the scattering effect of shielding materials. In practical complex multi-group problems, the MCS method can be independently applied in several groups to improve calculation accuracy.
ANNALS OF NUCLEAR ENERGY
(2021)
Article
Mathematics, Applied
Yuri A. Eremin, George Fikioris, Nikolaos L. Tsitsas, Thomas Wriedt
Summary: This paper introduces a new Method of Internal Auxiliary Source-Sinks (MIASS) for solving the two-dimensional interior Dirichlet acoustic problem for the Helmholtz equation. Two versions of MIASS, one for closed auxiliary curve (MIASS-C) and another for open auxiliary curve (MIASS-O), are provided with mathematical and numerical foundations. Completeness and linear independence of the discrete system of source-sinks are demonstrated along with indicative numerical results and discussion of numerical implementation aspects.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Multidisciplinary Sciences
Aryan Lall, Siddharth Tallur
Summary: Sequence alignment is crucial in bioinformatics to identify similarity between sequences, implying functional, structural or evolutionary relationships. Extending genome-based diagnostics to affordable healthcare requires algorithms that can operate on low-cost edge devices. This work presents EdgeAlign, a deep reinforcement learning method for performing pairwise DNA sequence alignment on stand-alone edge devices, achieving high compactness and deployed on two edge devices for demonstration.
SCIENTIFIC REPORTS
(2023)
Article
Mathematics, Applied
Yuri A. Eremin, Nikolaos L. Tsitsas, Minas Kouroublakis, George Fikioris
Summary: A new computational scheme of the Discrete Sources Method (DSM) is developed for the numerical solution of two-dimensional acoustic and electromagnetic transmission boundary-value problems. The new DSM scheme is established and shown to converge uniformly to the exact solution of the BVP. An analytic representation is derived for the calculation of the scattering cross section, and numerical results demonstrate the accuracy and efficiency of the new scheme.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Jan Glaubitz
Summary: This paper presents the derivation of provable positive and exact formulas using the method of least squares in a general multi-dimensional setting. By using a sufficiently large number of equidistributed data points, these formulas are ensured to be positive and exact. The paper also discusses the application of these provable positive and exact formulas in constructing nested stable high-order rules and positive interpolatory formulas.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2023)
Article
Mathematics, Applied
Kang Fu, Hongling Hu, Kejia Pan
Summary: A sixth order quasi-compact finite difference scheme for the Helmholtz equation with variable wave numbers in two and three dimensional rectangular domains is developed and analyzed in this paper. The scheme has explicit expressions for the finite difference coefficients and the weights of the source term without involving derivatives. The sixth order convergence of the new method is proven and confirmed through numerical experiments.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Computer Science, Interdisciplinary Applications
Na Zhang, Ahmad S. Abushaikha
Summary: This paper presents a fully implicit mimetic finite difference method (MFD) for general fractured reservoir simulation, extending this novel numerical discretization scheme to discrete fracture models. The MFD scheme supports general polyhedral meshes and full tensor properties, improving modeling and simulation of subsurface reservoirs. The paper also describes the principle of the MFD approach and presents numerical formulations of the discrete fracture model, demonstrating accuracy and robustness through case studies.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
Bao-Feng Feng, Han-Han Sheng, Guo-Fu Yu
Summary: In this paper, two integrable and one non-integrable semi-discrete analogues of a generalized sine-Gordon equation are constructed, using the Backlund transformation of bilinear equations and appropriate definition of the discrete hodograph transformation. N-soliton solutions in determinant form are obtained for the semi-discrete analogues. It is shown that the semi-discrete equations converge to the continuous generalized sine-Gordon equation in the continuous limit. Furthermore, four self-adaptive moving mesh methods are proposed for the generalized sine-Gordon equation, with numerical solutions demonstrating better performance compared to the Crank-Nicolson scheme.
NUMERICAL ALGORITHMS
(2023)
Article
Mathematics, Applied
H. A. Erbay, S. Erbay, A. Erkip
Summary: This study focuses on the numerical approximation of a general class of nonlinear unidirectional wave equations with a convolution-type nonlocality in space. A semi-discrete numerical method based on uniform space discretization and the discrete convolution operator is introduced to solve the Cauchy problem. The method is shown to be uniformly convergent as the mesh size approaches zero.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Computer Science, Information Systems
Yang Shi, Wei Chong, Wenhan Zhao, Shuai Li, Bin Li, Xiaobing Sun
Summary: In this paper, an innovative discrete time-variant recurrent neural network (I-DT-RNN) model is proposed for solving discrete time-variant matrix inversion problems. The model is mathematically founded on the second-order Taylor expansion and its reasonability and computational performance are validated through theoretical analysis and numerical experiments.
INFORMATION SCIENCES
(2024)
Article
Computer Science, Interdisciplinary Applications
Shijin Wang, Ruochen Wu, Feng Chu, Jianbo Yu
Summary: This paper studies an unrelated parallel machine scheduling problem with the consideration of order acceptance, sequence and machine-dependent setup times, and the maximum available times of machines. The goal is to maximize profit by finding the best job acceptance and scheduling. A mixed integer programming (MIP) model is formulated and a two-layer logic-based Benders decomposition (LBBD) method is developed to efficiently solve the problem. Extensive computational experiments show that the developed TL-LBBD method produces better quality solutions in significantly less computation time compared to the MIP model and classic LBBD method. The maximum scales of problem instances that can be optimally solved within 30 minutes by the TL-LBBD method are also evaluated.
COMPUTERS & INDUSTRIAL ENGINEERING
(2023)
Article
Mathematics, Applied
Nobuyuki Kato, Masashi Misawa, Yoshihiko Yamaura
Summary: In this paper, the regularity of a parabolic p-Laplacian system (p > 2) is studied using the discrete Morse flow method, known as a way to approximate solutions to parabolic partial differential equations. The approximate solution is constructed from a sequence of minimizers of variational functionals, with Euler-Lagrange equations being the time-discretized p-Laplacian system. The aim is to establish that regularity estimates for the approximate solution hold uniformly on two approximation parameters and demonstrate strong convergence.
ANNALI DI MATEMATICA PURA ED APPLICATA
(2021)
