Designing Effective Derivative Line Filters: Utilizing convolution to extract extra information

Sammanfattning: The ability to generate accurate approximations of derivatives holds significant importance in numerous scientific fields, including chemistry, economics and fluid mechanics. This thesis is centred around extracting hidden information in data using Smoothness-Increasing Accuracy-Conserving (SIAC) filters. The target application is in calculating derivatives in simulations of fluid flow. SIAC filters are based on convolution. Because of the properties used to construct the convolution kernel, we are able to design post-processing filters that can extract extra derivative information with high accuracy. In the past, these filters have typically had a tensor-product structure, which requires multi-dimensional filtering. Because of this, the filtering process can be very computationally expensive. The goal of this thesis is to develop one-dimensional line filters that are able to extract the derivative information more efficiently. By utilizing line filters, we aim to significantly cut the computational cost of the filtering process, while also maintaining the high accuracy.