The multigrid method is used for coupled fluid-solid scattering discretized by linear finite elements. Numerical results show that using Krylov methods as smoothers allows coarser spaces than with standard smoothers, such as Jacobi and GaussSeidel. Block diagonal preconditioning for the 2 × 2 block diagonal matrix of the coupled system is also considered. Both multigrid and block diagonal preco...

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d ≥ 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their anti...

This paper deals with the two-dimensional problem of elastic wave scattering from a finite crack at the interface between a coated material layer and its substrate. By adopting the Fourier transform method and introducing the crack opening displacement function, the boundary value problem is simplified for numerically solving a system of Cauchy-type singular integral equations by means of Jacob...

Let Hg and Dg be the Siegel upper half plane and the generalized unit disk of degree g respectively. Let C be the Euclidean space of all h× g complex matrices. We present a partial Cayley transformation of Dg × C (h,g) onto Hg × C (h,g) which gives a partial bounded realization of Hg × C (h,g) as Dg × C . We prove that the canonical actions of the Jacobi group on Dg × C (h,g) and Hg × C (h,g) a...

We describe some stochastic control problems in financial engineering arising from the need to find investment strategies to optimize some goal. Typically, these problems are characterized by nonlinear Hamilton-Jacobi-Bellman partial differential equations, and often they can be reduced to linear PDEs with the Legendre transform of convex duality. One situation where this cannot be achieved is ...

A family of orthogonal systems of irrational functions on the semi-infinite interval is introduced. The proposed orthogonal systems are based on Jacobi polynomials through an irrational coordinate transform. This family of orthogonal systems offers great flexibility to match a wide range of asymptotic behaviors at infinity. Approximation errors by the basic orthogonal projection and various oth...

In this paper, the twisted Jacobi intersections which contains Jacobi intersections as a special case is introduced. We show that every elliptic curve over the prime field with three points of order 2 is isomorphic to a twisted Jacobi intersections curve. Some fast explicit formulae for twisted Jacobi intersections curves in projective coordinates are presented. These explicit formulae for addi...

commutative properties of four-dimensional generalized symmetric pseudo-riemannian manifolds were considered. specially, in this paper, we studied skew-tsankov and jacobi-tsankov conditions in 4-dimensional pseudo-riemannian generalized symmetric manifolds.