Article
Mathematics, Applied
L'Ubomir Banas, Andre Wilke
Summary: This paper presents a posteriori error estimates for a fully discrete time-implicit finite element approximation of the stochastic total variation flow (STVF) with additive space time noise. The estimates are derived first for an implementable fully discrete approximation of a regularized STVF. It is then shown that the derived a posteriori estimates remain valid for the unregularized flow with a perturbation term controlled by the regularization parameter. Based on these estimates, a pathwise algorithm for adaptive space-time refinement is proposed and numerical simulations for the regularized STVF are performed to demonstrate the behavior of the proposed algorithm.
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2022)
Article
Optics
Patrick C. Chaumet
Summary: The paper proposes two new methods (IDR(s) and GPBiCGstab(L)) for computing the electromagnetic diffraction of objects larger than the wavelength. It is found that IDR(s) can reduce computation time but may not converge in some cases, while GPBiCGstab(L) always converges and also reduces computation time compared to QMR, GPBiCG, and BiCGstab.
JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER
(2024)
Article
Computer Science, Theory & Methods
Filip Tronarp, Simo Sarkka, Philipp Hennig
Summary: This paper investigates the maximum a posteriori estimate under the class of nu times differentiable linear time-invariant Gauss-Markov priors, and obtains convergence rates and numerical examples related to it.
STATISTICS AND COMPUTING
(2021)
Article
Optics
Sam Reifenstein, Timothee Leleu, Timothy McKenna, Marc Jankowski, Myoung-Gyun Suh, Edwin Ng, Farad Khoyratee, Zoltan Toroczkai, Yoshihisa Yamamoto
Summary: The coherent Ising machine (CIM) is designed to efficiently solve the NP-hard Ising problem. In this study, the CIM algorithm and architecture have been extended to directly solve SAT and Max-SAT problems, resulting in a new technique called coherent SAT solver (CSS). The CSS has been implemented in three different ways and compared with other solvers, demonstrating competitive performance and potential for practical use.
ADVANCES IN OPTICS AND PHOTONICS
(2023)
Article
Mathematics, Applied
Tobias Jawecki
Summary: The study extends the polynomial Krylov techniques for approximating the matrix exponential to the case of associated phi-functions. A posteriori error bounds and estimates based on the defect of the Krylov approximation are considered, with discussions on computable error bounds and a comparison of new error bounds with existing ones. The relationship between the accuracy of error bounds and Ritz values of A is characterized, and effects of finite precision are taken into account.
NUMERICAL ALGORITHMS
(2022)
Article
Computer Science, Interdisciplinary Applications
Micah Kranz, Julian Kajo Luedeker, Benedikt Kriegesmann
Summary: The paper introduces a rigorous formulation of adjoint systems for robust design optimization. The presented approach allows for the optimization of any objective function by considering deformation and maximum stress as objectives subjected to random material stiffness and geometry. The method requires solving at most three additional adjoint systems per uncertain system response, regardless of the number of random variables. Despite the assumption of linearity with respect to random parameters, the approach is able to find robust designs according to the validation with Monte Carlo simulations.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2023)
Article
Computer Science, Interdisciplinary Applications
Ming Zhou, Ole Sigmund
Summary: The paper discusses Sigmund's 2001 educational paper with a self-contained 99-line MATLAB code, which has had a far-reaching impact on teaching and research of topology optimization. The goal of the paper is to provide clarity to the theoretical foundation and enable students to learn the complete iterative optimization solution with minimum additional effort.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)
Article
Mathematics, Applied
Yuji Nakatsukasa, Lloyd N. Trefethen
Summary: The article discusses the concept of reciprocal-log or log-lightning approximation, proving that errors decrease exponentially with the number of poles N and that near-best approximations have exponential or near-exponential convergence. These results are applied to derive a log-lightning method for numerically solving Laplace and related PDEs, showing near-exponential convergence in contrast to the original lightning methods based on rational functions.
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2021)
Article
Mathematics, Applied
Jianwei Zhou, Huiyuan Li, Zhimin Zhang
Summary: In this paper, the authors investigate a posteriori error estimates of the Galerkin spectral methods for second-order equations. They propose a simple type of error estimator based on the expansion coefficients of known quantities such as the right-hand term. The authors show that the decay rate of the high frequency coefficients of the right-hand term serves as an ideal a posteriori error estimator. They also establish a posteriori error estimates on the Galerkin spectral method applied to the singular perturbation problem, where the efficiency is given by the approximation errors of the weighted L-2-projection of the right-hand function and the reliability is determined by the truncation errors of the right-hand function together with the low frequency coefficients.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Physiology
Marta Borras, Judit Chamorro-Servent
Summary: Cardiac disease is a major cause of mortality in developed countries. ECGI technology is being developed to identify at-risk patients and provide accurate diagnosis and therapy guidance. Research shows that ART method achieved the most stable solutions and the ART, random ART, and RRGMRES methods can improve the accuracy of solutions compared to the GMRES method.
FRONTIERS IN PHYSIOLOGY
(2021)
Article
Mathematics, Applied
Fleurianne Bertrand, Gerhard Starke
Summary: The article presents a posteriori error estimates for the Biot problem using a three-field variational formulation, with H(div)-conforming reconstructions of stress and flux for guaranteed error bounds. Emphasis is placed on nearly incompressible materials, with error estimates holding uniformly even in the incompressible limit.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Computer Science, Interdisciplinary Applications
Fu Jiayi, Huang Hai
Summary: This study focuses on the discrete size and topology optimization problems for structures composed of different components. An optimization method based on approximate concepts is proposed, which determines topology variables using a genetic algorithm and optimizes discrete size variables. The results of numerical examples demonstrate the high efficiency of this method in solving discrete size and topology optimization problems.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2022)
Article
Computer Science, Software Engineering
Timo Berthold, Zsolt Csizmadia
Summary: This paper introduces the confined primal integral as a new performance measure, emphasizing the early part of the solution process. It provides a closed analytic formula and an incremental update formula to compute this measure. Experimental results show that using the confined primal integral can help determine the effectiveness of local solvers.
MATHEMATICAL PROGRAMMING
(2021)
Article
Mathematics, Applied
Fei Li, Nianyu Yi
Summary: In this paper, we present two goal-oriented a posteriori error estimates for the reaction-diffusion equation with a nonlinear reaction term, utilizing finite element approximations in the enriched space. The first error estimator provides rigorous global lower and upper bounds on the error in the quantity of interest, while the second one offers a simple and efficient computation. We propose corresponding goal-oriented adaptive finite element algorithms and demonstrate their effectiveness and comparable performance through a series of numerical experiments.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics
R. H. Al-Obaidi, M. T. Darvishi
Summary: In this paper, a new class of frozen Jacobian multi-step iterative methods is proposed to solve systems of nonlinear equations. The proposed algorithms exhibit a highly convergent order and excellent efficiency index. Theoretical analysis and numerical experiments are performed to demonstrate the performance of the proposed methods, compared with known algorithms from existing literature.
Article
Materials Science, Multidisciplinary
Jens Gravesen, Morten Willatzen
PHYSICA STATUS SOLIDI-RAPID RESEARCH LETTERS
(2019)
Article
Materials Science, Multidisciplinary
Anton Evgrafov, Jose C. Bellido
MATHEMATICS AND MECHANICS OF SOLIDS
(2019)
Article
Materials Science, Multidisciplinary
Jens Gravesen, Morten Willatzen
PHYSICA STATUS SOLIDI-RAPID RESEARCH LETTERS
(2019)
Article
Mathematics, Applied
Jose C. Bellido, Anton Evgrafov
Summary: This paper is a follow-up to a previous work where the H-convergence concept was extended to fractional p-Laplace type operators. It demonstrates that the weak-* convergence of coefficients is an equivalent condition for H-convergence of the sequence of nonlocal operators, which is in stark contrast to the local p-Laplacian case.
REVISTA MATEMATICA COMPLUTENSE
(2021)
Editorial Material
Mathematics, Applied
Anton Evgrafov, Ole Sigmund
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
(2020)
Article
Chemistry, Multidisciplinary
Jens Gravesen, Morten Willatzen
APPLIED SCIENCES-BASEL
(2020)
Article
Computer Science, Interdisciplinary Applications
A. Limkilde, A. Evgrafov, J. Gravesen, A. Mantzaflaris
Summary: Shape optimization based on isogeometric analysis (IGA) has gained popularity for its seamless integration into the CAD workflow, while facing challenges in maintaining the validity of geometry parameterization. A possible solution is to include both boundary and interior control points in the optimization problem, with the addition of a regularization term like the Winslow functional to ensure quality parameterization. This approach shows comparable performance to state-of-the-art methods, especially on coarse discretizations.
JOURNAL OF COMPUTATIONAL DESIGN AND ENGINEERING
(2021)
Article
Chemistry, Multidisciplinary
Jens Gravesen, Morten Willatzen, Jiajia Shao, Zhong Lin Wang
Summary: A general theoretical analysis of a 3D generic TENG structure is presented in this paper. It is found that the optimal TENG geometry is independent of the frequency of the moving dielectric, but the external ohmic impedance for maximum power output is inversely proportional to the frequency. The energy of the TENG is proportional to the cube of its size, the square of the triboelectric charge density, and the angular frequency of the moving dielectric.
ADVANCED FUNCTIONAL MATERIALS
(2022)
Article
Computer Science, Software Engineering
Jens Gravesen, Peter Nortoft
Summary: The study focuses on constraints on surface curvature in engineering design, proposing a new method to globally check the principal curvatures of a spline surface. This method reformulates the curvature validity condition into three polynomial expressions, allowing for direct assessment of global curvature validity. The applicability of the method is demonstrated on various surfaces including a paraboloid, a bi-linear surface, and an industry-oriented reflector antenna surface on a satellite.
COMPUTER-AIDED DESIGN
(2022)
Article
Chemistry, Physical
Jens Gravesen, Morten Willatzen, Jiajia Shao, Zhong Lin Wang
Summary: This article provides a detailed mathematical analysis and fast computational method for designing spherical TENG devices to achieve optimal performance. It is found that the difference between the assumptions of a uniform potential vs. uniform charge density on electrodes for spherical TENG model parameters increases with the spatial dimensions of the electrodes.
Article
Chemistry, Physical
Jens Gravesen, Morten Willatzen, Jiajia Shao, Zhong Lin Wang
Summary: A detailed geometric analysis of spherical triboelectric nanogenerators is presented in this study. Compared to previous research on spherical triboelectric generators, the general case where the moving dielectric rolls on the inside surface of the larger sphere of the TENG is discussed in terms of maximum energy harvesting. Optimization analysis of geometrical parameters allows for the solution of various cases of electrode geometry, such as spherical circle, spherical ellipse, spherical rectangle, or spherical isosceles trapezium. The analytical insight and computational effectiveness provided by differential geometry make the mathematical model superior to standard 3D numerical methods.
Article
Mathematics, Applied
Anton Evgrafov, Jose C. Bellido
Summary: This paper examines the optimal distribution problem for a limited amount of conductive material in systems governed by local and nonlocal scalar diffusion laws. The limiting case when the available material approaches zero is of theoretical and practical interest and continues to be actively studied. The local case poses challenges in both analytical and numerical aspects due to the vector-valued Radon measures, while the nonlocal case allows solutions in Lebesgue spaces with mixed exponents. By disregarding the antisymmetry requirement on the two-point fluxes, the nonlocal problem provides a one-sided estimate for the corresponding local measure-valued optimal design problem, which can be transformed into a true limiting process through duality and generalization of nonlocal characterizations of Sobolev spaces to mixed Lebesgue exponents.
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
(2023)
Article
Automation & Control Systems
Anton Evgrafov, Jose C. Bellido
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2020)