We study the ability of high order numerical methods to propagate discrete waves at the same speed as the physical waves in the case of the one-way wave equation. A detailed analysis of the finite element method is presented including an explicit form for the discrete dispersion relation and a complete characterisation of the numerical Bloch waves admitted by the scheme. A comparision is made w...

In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that the n-dimensional hypersurface, Γ ⊂ Rn+1, is embedded in a polyhedral domain in Rn+1 consisting of a union, Th, of (n+ 1)-simplices. The unifying feature of the methodological approach is that the finit...

The Hermitian Lanczos method for Hermitian matrices has a wellknown connection with a 3-term recurrence for polynomials orthogonal on a discrete subset of R. This connection disappears for normal matrices with the Arnoldi method. In this paper we consider an iterative method that is more faithful to the normality than the Arnoldi iteration. The approach is based on enlarging the set of polynomi...

In an earlier article, atomic radii of elements of Groups 1A 8A were shown to be proportional to their Bohr radii obtained from the first ionization potentials and the constants of proportionality were shown to be simple functions of the Golden ratio. Here it is shown that the above finding holds also for elements of Groups 1B 8B including Lanthanides and Actinides. All the relevant data are pr...

The presented work introduces a novel cancelation technique, based on the linear superposition of stationary crossflow instabilities (CFI) through application streamwise series optimally positioned discrete roughness elements (DRE) arrays swept wing surface. DRE are designed and arranged with suitable amplitude phase shift to induce velocity disturbance systems that destructively interact, ulti...

There are q+q right PGL2(Fq)−cosets in the group PGL2(Fq2). In this paper, we present a method of generating all the coset representatives, which runs in time Õ(q), thus achieves the optimal time complexity up to a constant factor. Our algorithm has applications in solving discrete logarithms and finding primitive elements in finite fields of small characteristic.