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Non-overlapping Schwarz methods with generalized Robin transmission conditions were originally introduced by B. Despr\'es for time-harmonic wave propagation problems and have largely developed over the past thirty years. The aim of the…
Recently, Garcke et al.[Garcke, Hinze, Kahle, A stable and linear time discretization for a thermodynamically consistent model for two-phase incompressible flow, Applied Numerical Mathematics 99, pp. 151-171, 2016] developed a consistent…
This paper considers a pair of coupled nonlinear Helmholtz equations \begin{align*} -\Delta u - \mu u = a(x) \left( |u|^\frac{p}{2} + b(x) |v|^\frac{p}{2} \right)|u|^{\frac{p}{2} - 2}u, \end{align*} \begin{align*} -\Delta v - \nu v = a(x)…
We consider the inverse problem of reconstructing general solutions to the Helmholtz equation on some domain $\Omega$ from their values at scattered points $x_1,\dots,x_n\subset \Omega$. This problem typically arises when sampling acoustic…
The Richards equation is a nonlinear parabolic equation that is commonly used for modelling saturated/unsaturated flow in porous media. We assume that the medium occupies a bounded Lipschitz domain partitioned into two disjoint subdomains…
Harmonic maps are important in generating parameterizations for various domains, particularly in two and three dimensions. General extensions of two-dimensional harmonic parameterizations for volumetric parameterizations are known to fail…
The displacement field for three dimensional dynamic elasticity problems in the frequency domain can be decomposed into a sum of a longitudinal and a transversal part known as a Helmholtz decomposition. The Cartesian components of both the…
A discretization scheme for variable coefficient Helmholtz problems on two-dimensional domains is presented. The scheme is based on high-order spectral approximations and is designed for problems with smooth solutions. The resulting system…
There are significant differences between Helmholtz and Hodge's decomposition theorems, but both share a common flavor. This paper is a first step to bring them together. We here produce Helmholtz theorems for differential 1-forms and…
To derive the convergence field from the gravitational shear (gamma) of the background galaxy images, the classical methods require a convolution of the shear to be performed over the entire sky, usually expressed thanks to the Fast Fourier…
This paper introduces a class of approximate transparent boundary conditions for the solution of Helmholtz-type resonance and scattering problems on unbounded domains. The computational domain is assumed to be a polygon. A detailed…
This article extends the theorem of the absence of wandering domains from unimodal maps to infinitely period-doubling renormalizable H\'enon-like maps in the strongly dissipative (area contracting) regime. The theorem solves an open problem…
Domain decomposition methods are widely used for the numerical solution of partial differential equations on high performance computers. We develop an adjoint-based a posteriori error analysis for both multiplicative and additive…
Existing results on decomposition methods and algorithms for nonconvex problems are minimal. Parallel decomposition algorithms do not exist for nonconvex problems with coupling nonlinear equality constraints. Besides, decomposition…
Sweeping is a commonly used procedure to explicitly solve the discrete ordinates equation, which itself is a common approximation of the neutron transport equation. To sweep through the computational domain, an ordering of the spatial cells…
The Neumann--Neumann method is a commonly employed domain decomposition method for linear elliptic equations. However, the method exhibits slow convergence when applied to semilinear equations and does not seem to converge at all for…
We consider a variational method to solve the optical flow problem with varying illumination. We apply an adaptive control of the regularization parameter which allows us to preserve the edges and fine features of the computed flow. To…
An iteration-free method of domain decomposition is considered for approximate solving a boundary value problem for a second-order parabolic equation. A standard approach to constructing domain decomposition schemes is based on a partition…
Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…
We consider the leapfrog algorithm by Noakes for computing geodesics on Riemannian manifolds. The main idea behind this algorithm is to subdivide the original endpoint geodesic problem into several local problems, for which the endpoint…