Essays about: "Poisson s equation"

Showing result 1 - 5 of 8 essays containing the words Poisson s 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. 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

4. 3. 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

5. 4. Solving Partial Differential Equations With Neural Networks

   University essay from Uppsala universitet/Matematiska institutionen

   Author : Håkan Karlsson Faronius; [2023]
   Keywords : Partial differential equations; neural networks; physics-informed neural networks; deep ritz method; fourier neural operator; importance sampling; inverse problems;

   Abstract : In this thesis three different approaches for solving partial differential equa-tions with neural networks will be explored; namely Physics-Informed NeuralNetworks, Fourier Neural Operators and the Deep Ritz method. Physics-Informed Neural Networks and the Deep Ritz Method are unsupervised machine learning methods, while the Fourier Neural Operator is a supervised method. READ MORE

6. 5. Towards an Efficient Spectral Element Solver for Poisson’s Equation on Heterogeneous Platforms

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

   Author : Jonas Nylund; [2022]
   Keywords : Neko; CUDA; Heterogeneous hardware; GPU; Gather-Scatter; HPC; CFD; Neko; CUDA; Heterogena plattformar; GPU; Gather-Scatter; Högprestandabe-räkningar; Beräkningsströmningsdynamik;

   Abstract : Neko is a project at KTH to refactor the widely used fluid dynamics solver Nek5000 to support modern hardware. Many aspects of the solver need adapting for use on GPUs, and one such part is the main communication kernel, the Gather-Scatter (GS) routine. To avoid race conditions in the kernel, atomic operations are used, which can be inefficient. READ MORE