Helmholtz Scattering by Random Domains: First-Order Sparse Boundary Element Approximation

Invariant Domains and First-Order Continuous Finite Element Approximation for Hyperbolic Systems

We propose a numerical method to solve general hyperbolic systems in any space dimension using forward Euler time stepping and continuous finite elements on non-uniform grids. The properties of the method are based on the introduction of an artificial dissipation that is defined so that any convex invariant sets containing the initial data is an invariant domain for the method. The invariant do...

Sea Surfaces Scattering by Multi-Order Small-Slope Approximation: a Monte-Carlo and Analytical Comparison

L-band electromagnetic scattering from two-dimensional random rough sea surfaces are calculated by first- and second-order Small-Slope Approximation (SSA1, 2) methods. Both analytical and numerical computations are utilized to calculate incoherent normalized radar cross-section (NRCS) in mono- and bi-static cases. For evaluating inverse Fourier transform, inverse fast Fourier transform (IFFT) i...

Finite element approximation of fractional order elliptic boundary value problems

A finite element numerical method is investigated for fractional order elliptic boundary value problems with homogeneous Dirichlet type boundary conditions. It is pointed out that an appropriate stiffness matrix can be obtained by taking the prescribed fractional power of the stiffness matrix corresponding to the non-fractional elliptic operators. It is proved that this approach, which is also ...

Autoregressive Gaussian Random Vectors of First Order

First-Order Definability of Trees and Sparse Random Graphs

Let D(G) be the smallest quantifier depth of a first order formula which is true for a graph G but false for any other non-isomorphic graph. This can be viewed as a measure for the descriptive complexity of G in first order logic. We show that almost surely D(G) = Θ( ln n ln ln n ), where G is a random tree of order n or the giant component of a random graph G(n, c n ) with constant c > 1. Thes...