TY - JOUR AU - Tarcsay, Zsigmond AU - Sebestyén, Zoltán TI - Reduction of positive self-adjoint extensions JF - OPUSCULA MATHEMATICA J2 - OPUSC MATHEMATICA VL - 44 PY - 2024 IS - 3 SP - 425 EP - 438 PG - 14 SN - 1232-9274 DO - 10.7494/OpMath.2024.44.3.425 UR - https://m2.mtmt.hu/api/publication/34751048 ID - 34751048 N1 - Zsigmond Tarcsay was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the ÚNKP–22-5-ELTE-1096 New National Excellence Program of the Ministry for Innovation and Technology. LA - English DB - MTMT ER - TY - JOUR AU - Sikolya, Eszter TI - Reaction-diffusion equations on metric graphs with edge noise JF - ANALYSIS MATHEMATICA J2 - ANAL MATH PY - 2024 SN - 0133-3852 DO - 10.1007/s10476-024-00006-z UR - https://m2.mtmt.hu/api/publication/34749280 ID - 34749280 AB - We investigate stochastic reaction-diffusion equations on finite metric graphs. On each edge in the graph a multiplicative cylindrical Gaussian noise driven reaction-diffusion equation is given. The vertex conditions are the standard continuity and generalized, non-local Neumann-Kirchhoff-type law in each vertex. The reaction term on each edge is assumed to be an odd degree polynomial, not necessarily of the same degree on each edge, with possibly stochastic coefficients and negative leading term. The model is a generalization of the problem in [14] where polynomials with much more restrictive assumptions are considered and no first order differential operator is involved. We utilize the semigroup approach from [15] to obtain existence and uniqueness of solutions with sample paths in the space of continuous functions on the graph. LA - English DB - MTMT ER - TY - JOUR AU - Fekete, Imre AU - Molnár, András Sándor AU - Simon L., Péter TI - A Functional Approach to Interpreting the Role of the Adjoint Equation in Machine Learning JF - RESULTS IN MATHEMATICS J2 - RES MATHEM VL - 79 PY - 2024 IS - 1 SN - 1422-6383 DO - 10.1007/s00025-023-02074-3 UR - https://m2.mtmt.hu/api/publication/34435578 ID - 34435578 AB - The connection between numerical methods for solving differential equations and machine learning has been revealed recently. Differential equations have been proposed as continuous analogues of deep neural networks, and then used in handling certain tasks, such as image recognition, where the training of a model includes learning the parameters of systems of ODEs from certain points along their trajectories. Treating this inverse problem of determining the parameters of a dynamical system that minimize the difference between data and trajectory by a gradient-based optimization method presents the solution of the adjoint equation as the continuous analogue of backpropagation that yields the appropriate gradients. The paper explores an abstract approach that can be used to construct a family of loss functions with the aim of fitting the solution of an initial value problem to a set of discrete or continuous measurements. It is shown, that an extension of the adjoint equation can be used to derive the gradient of the loss function as a continuous analogue of backpropagation in machine learning. Numerical evidence is presented that under reasonably controlled circumstances the gradients obtained this way can be used in a gradient descent to fit the solution of an initial value problem to a set of continuous noisy measurements, and a set of discrete noisy measurements that are recorded at uncertain times. LA - English DB - MTMT ER - TY - JOUR AU - Matebie, Teshome Bayleyegn AU - Faragó, István AU - Havasi, Ágnes TI - On the convergence of multiple Richardson extrapolation combined with explicit Runge–Kutta methods JF - PERIODICA MATHEMATICA HUNGARICA J2 - PERIOD MATH HUNG PY - 2024 SN - 0031-5303 DO - 10.1007/s10998-023-00557-y UR - https://m2.mtmt.hu/api/publication/34396234 ID - 34396234 N1 - Export Date: 7 December 2023 Correspondence Address: Havasi, Á.; HUN-REN-ELTE Numerical Analysis and Large Networks Research Group, Pázmány Péter s. 1/C, Hungary; email: agnes.havasi@ttk.elte.hu AB - The order of accuracy of any convergent time integration method for systems of differential equations can be increased by using the sequence acceleration method known as Richardson extrapolation, as well as its variants (classical Richardson extrapolation and multiple Richardson extrapolation). The original (classical) version of Richardson extrapolation consists in taking a linear combination of numerical solutions obtained by two different time-steps with time-step sizes h and h /2 by the same numerical method. Multiple Richardson extrapolation is a generalization of this procedure, where the extrapolation is applied to the combination of some underlying numerical method and the classical Richardson extrapolation. This procedure increases the accuracy order of the underlying method from p to p+2 p + 2 , and with each repetition, the order is further increased by one. In this paper we investigate the convergence of multiple Richardson extrapolation in the case where the underlying numerical method is an explicit Runge–Kutta method, and the computational efficiency is also checked. LA - English DB - MTMT ER - TY - JOUR AU - Tarcsay, Zsigmond AU - Göde, Ábel TI - Operators on anti-dual pairs. Supremum and infimum of positive operators TS - Supremum and infimum of positive operators JF - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS J2 - J MATH ANAL APPL VL - 531 PY - 2024 IS - Issue 2, Part 2 PG - 11 SN - 0022-247X DO - 10.1016/j.jmaa.2023.127893 UR - https://m2.mtmt.hu/api/publication/34317106 ID - 34317106 N1 - Zs. Tarcsay was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the ÚNKP–22-5-ELTE-1096 New National Excellence Program of the Ministry for Innovation and Technology LA - English DB - MTMT ER - TY - JOUR AU - Karátson, János AU - Sysala, S. AU - Béreš, M. TI - Quasi‐Newton variable preconditioning for nonlinear elasticity systems in 3D JF - NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS J2 - NUMER LINEAR ALGEBR VL - 31 PY - 2024 IS - 3 PG - 20 SN - 1070-5325 DO - 10.1002/nla.2537 UR - https://m2.mtmt.hu/api/publication/34226995 ID - 34226995 N1 - Department of Applied Analysis & ELKH-ELTE Numerical Analysis and Large Networks Research Group, Eötvös Loránd University, Budapest, Hungary Department of Analysis and Operations Research, Budapest University of Technology and Economics, Budapest, Hungary Department of Applied Mathematics and Computer Science, Institute of Geonics of the Czech Academy of Sciences, Ostrava, Czech Republic Department of Applied Mathematics, VSB–Technical University of Ostrava, Ostrava, Czech Republic Export Date: 2 November 2023 Correspondence Address: Karátson, J.; Department of Applied Analysis, Hungary; email: kajkaat@caesar.elte.hu AB - Quasi‐Newton iterations are constructed for the finite element solution of small‐strain nonlinear elasticity systems in 3D. The linearizations are based on spectral equivalence and hence considered as variable preconditioners arising from proper simplifications in the differential operator. Convergence is proved, providing bounds uniformly w.r.t. the FEM discretization. Convenient iterative solvers for linearized systems are also proposed. Numerical experiments in 3D confirm that the suggested quasi‐Newton methods are competitive with Newton's method. LA - English DB - MTMT ER - TY - JOUR AU - Castillo, S. J. AU - Karátson, János TI - Rates of robust superlinear convergence of preconditioned Krylov methods for elliptic FEM problems JF - NUMERICAL ALGORITHMS J2 - NUMER ALGORITHMS PY - 2024 SN - 1017-1398 DO - 10.1007/s11075-023-01663-1 UR - https://m2.mtmt.hu/api/publication/34209067 ID - 34209067 N1 - Department of Applied Analysis, Eötvös Loránd University, Budapest, Hungary Department of Applied Analysis & HUN-REN-ELTE Numerical Analysis and Large Networks Research Group, Eötvös Loránd University, Budapest, Hungary Department of Analysis and Operations Research, Budapest University of Technology and Economics, Budapest, Hungary Export Date: 8 November 2023 Correspondence Address: Karátson, J.; Department of Analysis and Operations Research, Hungary; email: kajkaat@caesar.elte.hu AB - This paper considers the iterative solution of finite element discretizations of second-order elliptic boundary value problems. Mesh independent estimations are given for the rate of superlinear convergence of preconditioned Krylov methods, involving the connection between the convergence rate and the Lebesgue exponent of the data. Numerical examples demonstrate the theoretical results. LA - English DB - MTMT ER - TY - JOUR AU - Huszty, Csaba György AU - Firtha, Gergely AU - Izsák, Ferenc TI - Symplectic time-domain finite element method (STD-FEM) extended with wave propagation in porous materials for automotive interior acoustic modeling JF - JOURNAL OF PHYSICS-CONFERENCE SERIES J2 - J PHYS CONF SER VL - 2677 PY - 2023 PG - 11 SN - 1742-6588 DO - 10.1088/1742-6596/2677/1/012010 UR - https://m2.mtmt.hu/api/publication/34429674 ID - 34429674 N1 - Conference code: 196045 Export Date: 26 January 2024 Funding details: 5/E5/DRTPM/IV/2023 Funding details: Kementerian Riset Teknologi Dan Pendidikan Tinggi Republik Indonesia Funding text 1: The Ministry of Research, Technology, and Higher Education (RISTEKDIKTI), Republic of Indonesia has supported this research via “Penelitian Dasar Unggulan Perguruan Tinggi 2023” with the number of contract 5/E5/DRTPM/IV/2023. AB - The prediction of sound field evolving inside automotive interiors has gained significant attention in recent years, both for acoustic design purposes and virtual reality applications. Recently, a novel numerical simulation method was proposed by the present authors termed as symplectic time-domain finite element method. This paper discusses the numerical method and its application for simulating sound fields inside vehicle interiors. The presented case study includes the effect of seat absorption and non-rigid boundaries by applying either locally reacting, or elastic surface models exhibiting extended reactivity. © Published under licence by IOP Publishing Ltd. LA - English DB - MTMT ER - TY - JOUR AU - Izsák, Ferenc AU - Izsák, Rudolf TI - Neural-Network-Assisted Finite Difference Discretization for Numerical Solution of Partial Differential Equations JF - ALGORITHMS J2 - ALGORITHMS VL - 16 PY - 2023 IS - 9 SN - 1999-4893 DO - 10.3390/a16090410 UR - https://m2.mtmt.hu/api/publication/34121362 ID - 34121362 AB - A neural-network-assisted numerical method is proposed for the solution of Laplace and Poisson problems. Finite differences are applied to approximate the spatial Laplacian operator on nonuniform grids. For this, a neural network is trained to compute the corresponding coefficients for general quadrilateral meshes. Depending on the position of a given grid point x0 and its neighbors, we face with a nonlinear optimization problem to obtain the finite difference coefficients in x0. This computing step is executed with an artificial neural network. In this way, for any geometric setup of the neighboring grid points, we immediately obtain the corresponding coefficients. The construction of an appropriate training data set is also discussed, which is based on the solution of overdetermined linear systems. The method was experimentally validated on a number of numerical tests. As expected, it delivers a fast and reliable algorithm for solving Poisson problems. LA - English DB - MTMT ER - TY - CHAP AU - Huszty, Csaba György AU - Izsák, Ferenc TI - Symplectic time-domain finite element method (STD-FEM) for room acoustic modeling T2 - Proceedings Internoise 2023 PB - Institute of Noise Control Engineering of the USA CY - Washington DC T3 - INTER-NOISE and NOISE-CON Congress and Conference Proceedings, ISSN 0736-2935 PY - 2023 SP - 3089 EP - 3099 PG - 11 DO - 10.3397/IN_2023_0447 UR - https://m2.mtmt.hu/api/publication/34061273 ID - 34061273 LA - English DB - MTMT ER -