Searched for: subject%3A%22partial%255C+differential%255C+equations%22
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Bakker, Bo (author)
Data-driven approaches are a promising new addition to the list of available strategies for solving Partial Differential Equations (PDEs). One such approach, the Principal Component Analysis-based Neural Network PDE solver, can be used to learn a mapping between two function spaces, corresponding to a PDE. However, the practical limitations of...
bachelor thesis 2024
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Kiste, Amund (author)
Solving Partial Differential Equations (PDEs) in engineering such as Navier-Stokes is incredibly computationally expensive and complex. Without analytical solutions, numerical solutions can take ages to simulate at great expense. In order to reduce this cost, neural networks may be used to compute approximations of the solution for use during...
bachelor thesis 2024
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Lacombe, Pablo (author)
This paper presents a comprehensive exploration of a novel method combining Principal Component Analysis (PCA) and Neural Networks (NN) to efficiently solve Partial Differential Equations (PDEs), a fundamental challenge in modeling a wide range of real-world phenomena. Our research extends the work of Bhattacharya et al. by focusing on PCA for...
bachelor thesis 2024
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Agresti, A. (author), Veraar, M.C. (author)
In this paper we introduce the critical variational setting for parabolic stochastic evolution equations of quasi- or semi-linear type. Our results improve many of the abstract results in the classical variational setting. In particular, we are able to replace the usual weak or local monotonicity condition by a more flexible local Lipschitz...
journal article 2024
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Bettini, Andrea (author)
This thesis presents an energy-conservative data-driven approach in modelling the closure terms of the Navier-Stokes equations casted through the Variational Multiscale (VMS) framework. For context, the VMS framework is applied in designing stabilised finite element methods for multiscale phenomena in which stability is not guaranteed. Under...
master thesis 2023
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Verton, Max (author)
We analyze the spatially discretized version of the Allen-Cahn partial differential equation. The second order derivative is numerically approximated by a weighted infinite sum. The coefficients of this sum as well as the function f in the differential equation have got freedom inside determined restrictions. For this spatially discretized...
bachelor thesis 2023
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Böhm, Udo (author)
The stochastic FitzHugh-Nagumo equations are a system of stochastic partial differential equations that describes the propagation of action potentials along nerve axons. In the present work we obtain well-posedness and regularisation results for the FitzHugh-Nagumo equations with domain R^d. We begin by considering the weak critical variational...
master thesis 2023
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van Kan, J.J.I.M. (author), Segal, A. (author), Vermolen, Fred (author)
Partial differential equations are paramount in mathematical modelling with applications in engineering and science. The book starts with a crash course on partial differential equations in order to familiarize the reader with fundamental properties such as existence, uniqueness and possibly existing maximum principles. The main topic of the...
book 2023
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Agresti, A. (author), Veraar, M.C. (author)
In this paper we consider a class of stochastic reaction-diffusion equations. We provide local well-posedness, regularity, blow-up criteria and positivity of solutions. The key novelties of this work are related to the use transport noise, critical spaces and the proof of higher order regularity of solutions – even in case of non-smooth...
journal article 2023
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Hadjisotiriou, George (author)
Compositional simulation is computationally intensive for high-fidelity models due to thermodynamic equilibrium relations and the coupling of flow, transport and mass transfer. In this report, two methods for accelerated compositional simulation are outlined and demonstrated for a gas vaporization problem. The first method uses a proxy model...
master thesis 2022
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Titulaer, Björn (author)
Spatiotemporal stochastic processes have applications in various fields, but they can be difficult to numerically approximate in a reasonable time, in particular, in the context of statistical inference for large datasets. <br/>Recently, a new approach for efficient spatiotemporal statistical modeling has been proposed, where the space-time...
master thesis 2022
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Ul Haq, Rana (author)
Convection-dominated flow problems are well-known to have non-physical oscillations near steep gradients or discontinuities in the solution when solved with standard numerical methods, such as finite elements or finite difference methods. To overcome this limitation, algebraic flux correction (AFC) can be used, which is a stabilization method....
master thesis 2022
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Daemen, Mieke (author)
The main aim of the research presented in this report is investigating analytical methods to model fluid-structure interaction in large-scale offshore floating photovoltaics. The model that was attempted to be solved analytically is based on a model presented by Pengpeng Xu (2022).<br/>The dimensions in the equations were removed. Applying a...
bachelor thesis 2022
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Zegers, Samuel (author)
In several experiments, enzymes have shown an in increase in diffusivity in the presence of their substrate. The enhancement in diffusivity ranged from as low as 28% for urease to 80% in the case of alkaline phosphatase. There are two main competing theories. One asserts that catalytically driven boosts propel the enzyme forward in ‘leaps’,...
bachelor thesis 2022
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Oliveira de Almeida, S. (author), Chapiro, Grigori (author), Zitha, P.L.J. (author)
Electromagnetic (EM) heating is an emerging method for storing renewable energy, such as photovoltaic solar and wind electric power, into aquifers. We investigate how the captured energy increases the temperature of a prototypical deep aquifer for a six-month period and then to which extent the stored energy can be recovered during the...
journal article 2022
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Tosti Balducci, G.B.L. (author), Chen, B. Y. (author), Möller, M. (author), Gerritsma, M.I. (author), De Breuker, R. (author)
Structural mechanics is commonly modeled by (systems of) partial differential equations (PDEs). Except for very simple cases where analytical solutions exist, the use of numerical methods is required to find approximate solutions. However, for many problems of practical interest, the computational cost of classical numerical solvers running on...
review 2022
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Hendriks, Leo (author)
This essay shows a two dimensional implementation of the finite element method for the Westervelt equation. To do this the finite element method is first applied to the linear wave equation, then to non-linear diffusion and finally to the Westervelt equation. Both an element by element and a faster vectorized implementation are given for the...
bachelor thesis 2021
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Westdorp, Rik (author)
In this thesis, a variation on the nonlinear Schrödinger (NLS) equation with multiplicative noise is studied. In particular, we consider a stochastic version of the parametrically-forced nonlinear Schrödinger equation (PFNLS), which models the effect of linear loss and the compensation thereof by phase-sensitive amplification in pulse...
master thesis 2021
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Vural, Asya (author)
The porous medium equation $\dv{t}u=\dv{x}(k(u)\dv{x}u)$ is a non-linear degenerate parabolic partial differential equation. Consequently, existence and uniqueness of its solutions is not immediately evident.<br/>This bachelor thesis presents a detailed discussion of Atkinson's and Peletier's 1971 article ``Similarity profiles of flows through...
bachelor thesis 2021
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Leeuwis, Toby (author)
When transforming PDE problems using Fourier and Laplace transforms, we can find functions that represent the problem, and which can be used to determine properties of the problem. We define such functions as symbols $P(\lambda,z)$. In general, we define the class of symbols $S(L_t\times L_x)$ are all functions which are represented by a...
bachelor thesis 2021
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