Essays about: "Poisson s Equation"
Showing result 1 - 5 of 8 essays containing the words Poisson s Equation.
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1. Adjoint-based Formulation for Shape Optimization Problems in Computational Fluid Dynamics
University essay from KTH/Matematik (Avd.)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
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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)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
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3. Application of Physics-Informed Neural Networks for Galaxy Dynamics
University essay from Linnéuniversitetet/Institutionen för fysik och elektroteknik (IFE)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
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4. Solving Partial Differential Equations With Neural Networks
University essay from Uppsala universitet/Matematiska institutionenAbstract : 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
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5. Towards an Efficient Spectral Element Solver for Poisson’s Equation on Heterogeneous Platforms
University essay from KTH/Skolan för elektroteknik och datavetenskap (EECS)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