Full seismic waveform inversion of Europe and Western Asia: with optimally designed adaptive meshes

In Geodesy, the development of accurate Digital Elevation Models of the surface helps to provide height data for various applications in other Earth Science disciplines. These models are used as base models for studies. Geophysics can be a support science when providing base models for non-invasive studies inside the Earth. Such models can be...

Error Estimates for Finite Element Simulations Using Neural Networks

In this work residual error estimates are constructed using Neural Networks for Finite Element Method. These can be used to do adaptive mesh refinement. Two neural networks are developed the Multilayer Perceptron and the Transformer model. The error estimates are made for 1d poisson equations but the idea will generalise to higher dimensions as...

Error-estimate based adaptive mesh refinement: A user-independent approach for LES

Computational fluid dynamics (CFD) has become an indispensable tool in research and engineering. Even though the performance of computers is increasing at unfathomable speeds, the calculation of many fluid problems remains to be challenging. With the emerging widespread use of Large Eddy Simulation (LES), the computational cost of simulations...

Wavelet-Based Adaptive Mesh Refinement

Wavelets have been very popular in the field of image compression and noise reduction. Another interesting application is adaptive mesh refinement. There are many wavelets with various properties, which will have different effects on different applications. There is no consensus on which wavelet is the best option for adaptive mesh refinement....

Numerical study of adaptive mesh refinement applied to a third order minimum truncation error Active Flux method

In 2011 a relatively new type of numerical scheme has been introduced: Active Flux schemes. In this type of scheme an extra degree of freedom is added to the cell interfaces of a regular finite volume grid. This enables the use of non-conservative update methods for these additional variables, as conservation is automatically adhered to by the...

Computing the Spectrum of the Confined Hydrogen Atom

This thesis is about the numerical approximation of the spectrum of the confined hydrogen atom. The energy levels and wave functions of the hydrogen atom are modelled by the corresponding eigenvalues and eigenvectors of the Schrödinger equation with Coulomb potential. At first different discretisation techniques for the hydrogenic Schrödinger...