Article
Computer Science, Interdisciplinary Applications
Alessandro Comunian, Mauro Giudici
Summary: The Comparison Model Method is a relatively simple and computationally efficient approach for identifying the transmissivity of a confined aquifer, but it suffers from some classical drawbacks related to ill-posedness and ill-conditioning. The effectiveness of the method can be enhanced by introducing a factor to limit negative effects and by casting it in a tomographic framework.
COMPUTERS & GEOSCIENCES
(2021)
Article
Environmental Sciences
Hassan Smaoui, Lahcen Zouhri, Sami Kaidi
Summary: This study introduces a new mathematical model for identifying the HDT of a porous medium based on inverse problem-solving techniques. The model is shown to be practical through an integrated optimization algorithm.
Article
Mathematics, Applied
Shukai Du, Samuel N. Stechmann
Summary: This study proposes an adaptive-mesh inversion method for solving the inverse problem of radiative transfer. By simultaneously addressing the optimization problems of inversion and mesh adaptivity and utilizing a goal-oriented error estimator, the mesh-refinement process is guided efficiently to solve the inverse problem.
Article
Mathematics, Applied
Zhaonan Dong, Lorenzo Mascotto, Oliver J. Sutton
Summary: The novel residual-based a posteriori error estimator for the biharmonic problem in two and three dimensions gives an upper bound and a local lower bound on the error, with the lower bound being robust to local mesh size but not to local polynomial degree. The analysis is based on elliptic reconstruction and Helmholtz decomposition, showing explicit suboptimality in terms of polynomial degree that grows at most algebraically.
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2021)
Article
Mathematics, Applied
Navid Shekarchizadeh, Bilen Emek Abali, Emilio Barchiesi, Alberto Maria Bersani
Summary: A novel parameter determination technique is developed for material models in continuum mechanics aimed at describing metamaterials. An automatized optimization process is developed specifically for obtaining metamaterials parameters, which aims at minimizing a mechanically meaningful error function. The parameter identification procedure is tested for an exemplary extension experiment of a metamaterial, proving to be robust and reliable.
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
(2021)
Article
Mathematics, Applied
Huiqing Liao, Heping Ma
Summary: In this study, a Legendre-Galerkin Chebyshev collocation method is introduced for solving the parabolic inverse problem with control parameters. The method shows optimal convergence in L-2-norm for nonlinear terms and is implemented using explicit-implicit iterative approach. By constructing suitable basis functions and collocating the nonlinear terms at specific points, the method demonstrates efficiency and capability in solving complex problems.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Mathematics, Applied
Nguyen Huy Tuan, Tomas Caraballo, Phan Thi Khanh Van, Vo Van Au
Summary: This article investigates the nonlocal nonlinear reaction-diffusion system with final conditions and proposes a modified quasi-reversibility model to stabilize the ill-posed problem. Numerical results are provided to demonstrate the effectiveness of the method.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Mathematics, Applied
Si Yuan, Quan Yuan
Summary: This article introduces a new type of Galerkin finite element method for solving first-order initial-value problems. By using the adjoint equation, one degree of freedom can be eliminated from the test function, and then the condensed test function and condensed Galerkin element are constructed. Mathematical proof and numerical verification show that the condensed element produces super-convergent nodal solutions.
APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION
(2022)
Article
Mathematics, Applied
Mihai Bucataru, Liviu Marin
Summary: In this study, we investigate the acceleration of two iterative algorithms for accurate reconstruction of missing temperature and normal heat flux on an inaccessible boundary. The convergence of each algorithm is analyzed by considering the properties of the corresponding operator and determining the optimal value of the relaxation parameter. Numerical experiments confirm the effectiveness of the algorithms in reducing CPU time.
NUMERICAL ALGORITHMS
(2023)
Article
Mathematics, Applied
Jian Meng
Summary: This paper focuses on designing the discontinuous Galerkin method to discretize the non-selfadjoint and nonlinear interior transmission eigenvalue problem. The eigenvalues obtained from scattering data can be used for target identification and nondestructive testing. The spectral approximation of the discontinuous Galerkin method is proven, and the convergence of the approximate transmission eigenvalue is observed to be at order O(h(2l))(l=1). Numerical examples are provided to demonstrate the theoretical results and to investigate the influence of penalty parameters in the scheme, transmission eigenvalues on stratified media, and the inverse spectral problem.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Geosciences, Multidisciplinary
Shizuka Takai, Taro Shimada, Seiji Takeda, Katsuaki Koike
Summary: In order to accurately estimate the remediation of accidental groundwater contamination, this study develops a geostatistical method to jointly clarify the contaminant plume and transmissivity distributions using both head and contaminant concentration data. The proposed method was demonstrated to be applicable and effective through two numerical experiments in a two-dimensional heterogeneous confined aquifer. The use of contaminant concentration data was found to be key in accurately estimating the transmissivity, and the uncertainty of the contaminant plume evolution was successfully evaluated.
MATHEMATICAL GEOSCIENCES
(2023)
Article
Mathematics, Applied
Yu Lu, Meng Li
Summary: In this paper, a linearized L 1-Galerkin finite element method is proposed to solve the nonlinear coupled time-fractional prey-predator problem. The time-space error splitting technique is utilized in the convergence analysis to derive the unconditionally optimal L-2-norm error estimate of the numerical scheme. Additionally, the unconditional superclose and superconvergence results under the bilinear finite element are deduced in detail. Numerical examples are presented to demonstrate the accuracy of the proposed FEMs and the effectiveness of the fast algorithm.
COMPUTATIONAL & APPLIED MATHEMATICS
(2023)
Article
Medicine, General & Internal
Chih-Sheng Lin, Bing-Ru Peng, Hong-Bing Ma, Ke-Lin Chen, Tsung-Han Lin, Lung-Kwang Pan, Ya-Hui Lin
Summary: This study addressed the challenge of head and neck CT angiography by using IPA-based time-resolved imaging of contrast kinetics. By analyzing a group of 627 cerebral hemorrhage patients, the researchers developed a semi-empirical formula that accurately calculated the CTA number and achieved a high level of coincidence.
Article
Mathematics, Applied
A. Janmohammadi, J. Damirchi, S. M. Mahmoudi
Summary: This paper focuses on the construction of a space-dependent term of an unknown source in a stable manner in the field of inverse problems. Specifically, it addresses the recovery of the unknown source term in a one-dimensional fractional diffusion problem. The approach involves transforming the major problem into an equation of operator form and solving it using the Ritz-Galerkin method with shifted Bernoulli wavelets as basis functions. The inclusion of a regularization method in the numerical algorithm ensures a stable solution to the resulting linear system. Numerical examples are provided to validate the proposed algorithm's effectiveness and efficiency in the presence of noise.
MATHEMATICAL SCIENCES
(2022)
Article
Mathematics, Applied
Dinh Nho Hao, Tran Nhan Quyen, Nguyen Thanh Son
Summary: This work addresses an inverse problem in heat conduction equations, identifying the source term using a Crank-Nicolson Galerkin method. The convergence of finite dimensional regularized approximations and error bounds are proven, with numerical experiments supporting the theoretical findings.
APPLIED MATHEMATICS AND OPTIMIZATION
(2021)