arXiv subjects

Sanjay Kumar Khattri

Publications and source records attributed to Sanjay Kumar Khattri.

5 recordsLinked to original sources

arXiv2009

How to increase convergence order of Newton's method to $2\times m$?

We present a simple yet powerful technique for forming iterative methods of various convergence orders. Methods of various convergence orders (four, six, eight and ten) are formed through a modest modification of the classical Newton method. The technique can be easily implemented in existing software packages as suggested by the presented C$^{++}$ algorithm. Finally some problems are solved through the proposed algorithm.

math.NA↗

arXiv2006

Multiblock Grid Generation for Simulations in Geological Formations

Simulating fluid flow in geological formations requires mesh generation, lithology mapping to the cells, and computing geometric properties such as normal vectors and volume of cells. The purpose of this research work is to compute and process the geometrical information required for performing numerical simulations in geological formations. We present algebraic techniques, named Transfinite Interpolation, for mesh generation. Various transfinite interpolation techniques are derived from 1D projection operators. Many geological formations such as the Utsira formation (Torp and Gale, 2004; Khattri, Hellevang, Fladmark and Kvamme, 2006) and the Snohvit gas field (Maldal and Tappel, 2004) can be divided into layers or blocks based on the geometrical or lithological properties of the layers. We present the concept of block structured mesh generation for handling such formations.

math.DG↗

arXiv2006

Computationally Efficient Technique for Nonlinear Poisson-Boltzmann Equation

Discretization of non-linear Poisson-Boltzmann Equation equations results in a system of non-linear equations with symmetric Jacobian. The Newton algorithm is the most useful tool for solving non-linear equations. It consists of solving a series of linear system of equations (Jacobian system). In this article, we adaptively define the tolerance of the Jacobian systems. Numerical experiment shows that compared to the traditional method our approach can save a substantial amount of computational work. The presented algorithm can be easily incorporated in existing simulators.

math-ph↗

arXiv2006

Adaptive Quadrilateral Mesh in Curved Domains

Nonlinear elliptic system for generating adaptive quadrilateral meshes in curved domains is presented. Presented technique has been implemented in the C++ language. The included software package can write the converged meshes in the GMV and Matlab formats. Since, grid adaptation is required for numerically capturing important characteristics of a process such as boundary layers. So, the presented technique and the software package can be a useful tool.

math.AP↗

arXiv2006

Which are Better Conditioned Meshes Adaptive, Uniform, Locally Refined or Localised

Adaptive, locally refined and locally adjusted meshes are preferred over uniform meshes for capturing singular or localised solutions. Roughly speaking, for a given degree of freedom a solution associated with adaptive, locally refined and locally adjusted meshes is more accurate than the solution given by uniform meshes. In this work, we answer the question which meshes are better conditioned. We found, for approximately same degree of freedom (same size of matrix), it is easier to solve a system of equations associated with an adaptive mesh.

math.NA↗