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An iterative Finite Element method predicated on a linearisation of the weak form around a reference configuration is derived for general, three-dimensional, free-surface flows, including systems with moving contact lines. The method is a…
We investigate corrector estimates for the solutions of a thermoelasticity problem posed in a highly heterogeneous two-phase medium and its corresponding two-scale thermoelasticity model which was derived in an earlier paper by two-scale…
In this work we demonstrate the robustness of a real-space approach for the treatment of infinite systems described with periodic boundary conditions that we have recently proposed [J. Phys. Chem. Lett. 17, 7090]. In our approach we extract…
Correct radar data fusion depends on knowledge of the spatial transform between sensor pairs. Current methods for determining this transform operate by aligning identifiable features in different radar scans, or by relying on measurements…
We define a parametric variant of generalized Euler sums and construct contour integration to give some explicit evaluations of these parametric Euler sums. In particular, we establish several explicit formulas of (Hurwitz) zeta functions,…
A family of explicit modified Euler methods (MEMs) is constructed for long-time approximations of super-linear SODEs driven by multiplicative noise. The proposed schemes can preserve the same Lyapunov structure as the continuous problems.…
A method for the resummation of nonalternating divergent perturbation series is described. The procedure constitutes a generalization of the Borel-Pad\'{e} method. Of crucial importance is a special integration contour in the complex plane.…
This summary of the doctoral thesis provides a comprehensive formulation of the Extended Discrete Fourier Transform (EDFT), derived directly from the Fourier integral and its orthogonality properties. The method is obtained by solving…
The accurate computation of the electrostatic capacity of three dimensional objects is a fascinating benchmark problem with a long and rich history. In particular, the capacity of the unit cube has widely been studied, and recent advances…
The computational cost of the boundary-condition-enforced immersed boundary method (IBM) increases in the order of $\mathcal{O}(N^2)$ as the number of Lagrangian points, $N$, increases. This is due to the time-consuming calculation of the…
In our previous work [SIAM J. Sci. Comput. 43(3) (2021) B784-B810], an accurate hyper-singular boundary integral equation method for dynamic poroelasticity in two dimensions has been developed. This work is devoted to studying the more…
We investigate the two-dimensional elastostatic inclusion problem in an unbounded medium. Building on the recent developments for rigid inclusions \cite{Mattei:2021:EAS} and conductivity inclusions \cite{Jung:2021:SEL}, we extend these…
The evaluation of electrostatic energy for a set of point charges in a periodic lattice is a computationally expensive part of molecular dynamics simulations (and other applications) because of the long-range nature of the Coulomb…
In this work, we present a novel error analysis for recovering a spatially dependent diffusion coefficient in an elliptic or parabolic problem. It is based on the standard regularized output least-squares formulation with an $H^1(\Omega)$…
We present a spectrally accurate method for the rapid evaluation of free-space Stokes potentials, i.e. sums involving a large number of free space Green's functions. We consider sums involving stokeslets, stresslets and rotlets that appear…
Three dimensional field configuration has been simulated for a simple wire chamber consisting of one anode wire stretched along the axis of a grounded square cathode tube by solving numerically the boundary integral equation of the first…
We give some new methods for perfect reconstruction from frame and sampling erasures in finitely many steps. By bridging an erasure set we mean replacing the erased Fourier coefficients of a function with respect to a frame by appropriate…
A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated…
The need to Fourier transform data sets with irregular sampling is shared by various domains of science. This is the case for example in astronomy or sismology. Iterative methods have been developed that allow to reach approximate…
Electroactive polymers such as dielectric elastomers (DEs) have attracted significant attention in recent years. Computational techniques to solve the coupled electromechanical system of equations for this class of materials have…