Essays about: "Poisson equation"

Showing result 1 - 5 of 26 essays containing the words Poisson equation.

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

    University essay from KTH/Matematik (Avd.)

    Author : Anton Scotte; [2023]
    Keywords : ;

    Abstract : 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. READ MORE

  3. 2. Investigating the density evolution of charged particles inside a square domain

    University essay from Uppsala universitet/Institutionen för fysik och astronomi

    Author : Wenhan Zhou; [2023]
    Keywords : N-body problem; PINN;

    Abstract : In this work, I propose a hybrid particle simulator for charged particles. The simulator consists of a physics-informed neural network, which can handle arbitrary external electric fields with continuous coordinates by solving the Poisson equation, and a graph-based algorithm that computes the interacting forces between the particles. READ MORE

  4. 3. The data-driven CyberSpine : Modeling the Epidural Electrical Stimulation using Finite Element Model and Artificial Neural Networks

    University essay from KTH/Skolan för elektroteknik och datavetenskap (EECS)

    Author : Yu Qin; [2023]
    Keywords : Spinal Cord Injury; Epidural Electrical Stimulation; Computational Neuroscience; Finite Element Model; Artificial Intelligence; Optimal Transport; EMG; Muscle Activation; Ryggmärgsskada; Epidural Elektrisk Stimulering; Beräkningsneurovetenskap; Finita Elementmodellen; Artificiell Intelligens; Optimal Transport; EMG; Muskelaktivering;

    Abstract : Every year, 250,000 people worldwide suffer a spinal cord injury (SCI) that leaves them with chronic paraplegia - permanent loss of ability to move their legs. SCI interrupts axons passing along the spinal cord, thereby isolating motor neurons from brain inputs. To date, there are no effective treatments that can reconnect these interrupted axons. READ MORE

  5. 4. 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

  6. 5. 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