Fredrik Fryklund

My research is in numerical analysis and scientific computing, with a focus on fast, high-order integral equation methods for partial differential equations in complex and time-dependent geometries. A central theme of my work is to extend potential theory-based methods to settings where classical integral equation techniques are more difficult to apply, including problems with inhomogeneous source terms and time dependence. This requires the fast and accurate evaluation of both layer and volume potentials, often in geometries where straightforward discretizations would be prohibitively expensive. My work combines analysis of the underlying PDEs and their integral representations with the development of numerical algorithms that preserve high-order accuracy while remaining computationally efficient. Related aspects of this work include function extension and Fourier methods coupled systems of partial differential equations.