Sökning: "Laplace equation"

Visar resultat 1 - 5 av 19 uppsatser innehållade orden Laplace equation.

  1. 1. Image-driven simulation of brain tumors using a reaction-diffusion mathematical model

    Master-uppsats, Linköpings universitet/Avdelningen för medicinsk teknik

    Författare :Kristos Qiqi; [2023]
    Nyckelord :brain tumor; cancer; mathematical model; simulation; magnetic resonance images; hjärntumör; cancer; matematisk model; simulering; magnetresonanstomografi bilder;

    Sammanfattning : Brain tumors pose a big challenge in the field of neuro-oncology. Gliomas are the largest subgroup. Magnetic resonance imaging is a non-invasive tool for detecting and characterizing these tumors. Mathematical models, such as the reaction-diffusion equation, can be used for understanding the intricate behavior of gliomas. LÄS MER

  3. 2. Adjoint-based Formulation for Shape Optimization Problems in Computational Fluid Dynamics

    Master-uppsats, KTH/Matematik (Avd.)

    Författare :Anton Scotte; [2023]
    Nyckelord :;

    Sammanfattning : A continuous adjoint formulation for exterior optimization of Dirichlet data on the boundary for potential flow applications has been developed in this thesis. This has been performed by utilizing boundary integral methods for both the primal problem (Laplace’s equation) and for the corresponding adjoint equation (Poisson’s equation) on the unit disc. LÄS MER

  4. 3. The History of the Dirichlet Problem for Laplace’s Equation

    Kandidat-uppsats, Linköpings universitet/Analys och didaktik; Linköpings universitet/Tekniska fakulteten

    Författare :Måns Alskog; [2023]
    Nyckelord :Potential Theory; Dirichlet Problem; Laplace’s Equation; Complex Analysis; Potentialteori; Dirichletproblemet; Laplaces ekvation; komplex analys;

    Sammanfattning : This thesis aims to provide an introduction to the field of potential theory at an undergraduate level, by studying an important mathematical problem in the field, namely the Dirichlet problem. By examining the historical development of different methods for solving the problem in increasingly general contexts, and the mathematical concepts which were established to support these methods, the aim is to provide an overview of various basic techniques in the field of potential theory, as well as a summary of the fundamental results concerning the Dirichlet problem in Euclidean space. LÄS MER

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

    Master-uppsats, Lunds universitet/Matematik LTH

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

    Sammanfattning : 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. LÄS MER

  7. 5. Tug-of-War and the p-Laplace Equation : Exploring a Mathematical link between Game Theory and Nonlinear Elliptic PDE's

    Kandidat-uppsats, Umeå universitet/Institutionen för matematik och matematisk statistik

    Författare :Zackarias Chronéer; [2023]
    Nyckelord :p-Laplacian; tug-of-war;

    Sammanfattning : In this report the connection between p-harmonic functions and the tug-of-war game is presented and some applications are mentioned. Moreover, sufficient background information of solutions to the p-Laplace equation is given. And to finish, an example of the game is given with simulations. . LÄS MER