The Laplace-Beltrami system of nonlinear, elliptic, partial differential equations has utility in the generation of computational grids on complex and highly curved geometry. Discretization of this system using the finite element method accommodates unstructured grids, but generates a large, sparse, ill-conditioned system of nonlinear discrete equations. The use of the Laplace-Beltrami approach...

The R-linear Beltrami equation appears in applications, such as in the inverse problem of recovering the electrical conductivity distribution in the plane. In this paper, a new way to discretize the R-linear Beltrami equation is considered. This gives rise to large and dense R-linear systems of equations with structure. For their iterative solution, norm minimizing Krylov subspace methods are d...

We consider problems concerning the existence of solutions Beltrami equations and their convergence in complex plane. are mainly interested case when these satisfy so-called hydrodynamic normalization condition neighborhood infinity. Under some conditions on dilatations inverse mappings, we have established such class continuous Sobolev mappings. also obtained results locally uniform limit a se...

We study the problem of Michell trusses when the system of applied equilibrated forces is a vector measure with compact support. We introduce a class of stress tensors which can be written as a superposition of rank-one tensors carried by curves (lines of principal strains). Optimality conditions are given for such families showing in particular that optimal stress tensors are carried by mutual...

It is proved that the action for nonlinear Beltrami equation (quasi-classical ¯ ∂-problem) evaluated on its solution gives a τ-function for dis-persionless KP hierarchy. Infinitesimal transformations of τ-function corresponding to variations of ¯ ∂-data are found. Determinant equations for the function generating these transformations are derived. They represent a dispersionless analogue of sin...

We construct solutions of the magnetohydrostatic (MHS) equations in bounded domains and on torus three spatial dimensions, as infinite time limits Voigt approximations viscous, non-resistive incompressible magnetohydrodynamics equations. The modify evolution without introducing artificial viscosity. show that obtained MHS are regular, nontrivial, not Beltrami fields.