Essays about: "pdes"

Showing result 1 - 5 of 36 essays containing the word pdes.

  1. 1. Symmetry in a free boundary problem

    University essay from KTH/Matematik (Avd.)

    Author : Seuri Basilio Kuosmanen; [2023]
    Keywords : Analysis of PDEs; Bernoulli-type boundary condition; free boundary problem; Laplacian operator; method of moving planes; symmetry; Analys av PDEs; Bernoulli-typ randvärde; frirandsproblem; Laplaceoperatorn; moving-plane metoden; symmetri;

    Abstract : We consider a variational formulation of a Bernoulli-type free boundary problem for the Laplacian operator with discontinuous boundary data. We show the existence of a weak solution to the problem. Moreover, we show that the solution has symmetry properties inherited by symmetric data. READ MORE

  3. 2. Evaluation of Physics Informed Neural Networks in engineering simple structural analysis problems

    University essay from Uppsala universitet/Institutionen för informationsteknologi

    Author : Georgios Nentidis; [2023]
    Keywords : ;

    Abstract : Neural Networks have found many applications for a long time in Machine Learning in different disciplines, and have especially flourished in the last decade because of the ever-increasing processing power especially from GPUs. Because of their ability to operate as universal function approximators and model nonlinear processes, attempts have been made in recent years to be also used for modeling partial differential equation (PDE) solutions. READ MORE

  4. 3. Improved Statistical Methods for Elliptic Stochastic Homogenization Problems : Application of Multi Level- and Multi Index Monte Carlo on Elliptic Stochastic Homogenization Problems

    University essay from Uppsala universitet/Tillämpad beräkningsvetenskap

    Author : Khalil Daloul; [2023]
    Keywords : Homogenization; Multilevel Monte Carlo; Multi-Index Monte Carlo; Monte Carlo; Multiscale methods;

    Abstract : In numerical multiscale methods, one relies on a coupling between macroscopic model and a microscopic model. The macroscopic model does not include the microscopic properties that the microscopic model offers and that are vital for the desired solution. READ MORE

  5. 4. Application of Physics-Informed Neural Networks for Galaxy Dynamics

    University essay from Linnéuniversitetet/Institutionen för fysik och elektroteknik (IFE)

    Author : Lucas Barbier; [2023]
    Keywords : ;

    Abstract : Developing efficient and accurate numerical methods to simulate dynamics of physical systems has been an everlasting challenge in computational physics. Physics-Informed Neural Networks (PINNs) are neural networks that encode laws of physics into their structure. READ MORE

  6. 5. Implementation and study of boundary integral operators related to PDE:s in the plane

    University essay from Lunds universitet/Matematik LTH

    Author : Erik Andersson; [2023]
    Keywords : Boundary integral equation; Singular integral operator; Product integration; Close evaluation; Numerical integration; MATLAB; Mathematics and Statistics;

    Abstract : The method of solving boundary value problems of partial differential equations numerically by first reformulating the problem as a boundary integral equation has many advantages over other methods, but also some unique difficulties. Some of these difficulties stem from problems in evaluating singular or nearly singular integral operators, and solving these difficulties is an active field of research. READ MORE