# G. Murali Mohan ReddyUniversity of São Paulo | USP · Department of Applied Mathematics and Statistics (SME) (São Carlos)

G. Murali Mohan Reddy

Ph.d.

## About

17

Publications

1,956

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93

Citations

Citations since 2016

Introduction

Gujji Murali Mohan Reddy currently works at the Department of Applied Mathematics and Statistics (SME) (São Carlos), University of São Paulo. Gujji does research in Applied Mathematics.

Additional affiliations

October 2014 - present

July 2008 - January 2014

Education

July 2008 - June 2014

## Publications

Publications (17)

We develop a novel phase-wise sequential numerical approach based on the method of fundamental solutions (MFS) for inverse two-phase nonlinear Stefan and Cauchy-Stefan problems in one dimension (1D). By treating each phase independently, the inverse two-phase nonlinear Stefan problem splits into two single-phase inverse problems: an inverse nonline...

Residual-based anisotropic a posteriori error estimates are derived for the parabolic integro-differential equation (PIDE) with smooth kernel in two-dimensions. Based on C 0-conforming piecewise linear elements for spatial discretization, the fully discrete method is achieved after discretizing in time by a two-step backward difference (BDF-2) form...

The efficient numerical solution of the one-phase linear inverse Stefan and Cauchy–Stefan problems is a delicate task owing to the problems' susceptibility to the perturbation of the given data. In this context, heuristic a posteriori error indicators are constructed for such inverse problems with noisy data in two dimensions (2D). Given a fixed co...

In this article, we study a novel computational technique for the efficient numerical solution of the inverse boundary identification problem with uncertain data in two dimensions. The method essentially relies on a posteriori error indicators consisting of the Tikhonov regularized solutions obtained by the method of fundamental solutions (MFS) and...

In this article, finite element a posteriori error estimates for the linear parabolic integro-differential equation using the two-step backward time descretization formula are explored. For space discretization, we use piecewise linear finite element spaces. The Ritz–Volterra reconstruction operator is used as a raw ingredient to obtain the optimal...

In this paper, a recent algorithm, based around the method of fundamental solutions (MFS), for reconstructing boundary data in inverse Stefan problems is extended and applied to inverse Cauchy–Stefan problems, wherein initial data must also be reconstructed. A key feature of the algorithm is that it is adaptive and iterates to find the optimal loca...

Although two-dimensional (2D) parabolic integro-differential equations (PIDEs) arise in many physical contexts, there is no generally available software that is able to solve them numerically. To remedy this situation, in this article, we provide a compact implementation for solving 2D PIDEs using the finite element method (FEM) on unstructured gri...

We study a posteriori error analysis for the space-time discretizations of linear parabolic integro-differential equation in a bounded convex polygonal or polyhedral domain. The piecewise linear finite element spaces are used for the space discretization, whereas the time discretization is based on the Crank–Nicolson method. The Ritz–Volterra recon...

In this exposition, a simple practical adaptive algorithm is developed for ef- ficient and accurate reconstruction of Neumann boundary data in the inverse Stefan problem, which is a highly nontrivial task. Primarily, this algorithm detects the satisfactory location of the source points from the boundary in reconstructing the boundary data in the in...

The perspective 3-point (P3P) problem, also known as pose estimation, has its origins in camera calibration and is of importance in many fields: for example, computer animation, automation, image analysis, and robotics. One possibility is to formulate it mathematically in terms of finding the solution to a quartic equation. However, there is yet no...

Current practice in the use of the method of fundamental solutions (MFS) for inverse Stefan problems typically involves setting the source and collocation points at some distance, h, from the boundaries of the domain in which the solution is required, and then varying their number, (Formula presented.), so that the obtained solution fulfils a desir...

We derive residual-based a posteriori error estimates of finite element method for linear parabolic interface problems in a two-dimensional convex polygonal domain. Both spatially discrete and fully discrete approximations are analyzed. While the space discretization uses finite element spaces that are allowed to change in time, the time discretiza...

This paper studies a residual-based a posteriori error estimates for linear parabolic interface problems in a bounded convex polygonal domain in (Formula presented.). We use the standard linear finite element spaces in space which are allowed to change in time and the two-step backward differentiation formula (BDF-2) approximation at equidistant ti...

We derive two optimal a posteriori error estimators for an implicit fully discrete approximation to the solutions of linear integro-differential equations of the parabolic type. A continuous, piecewise linear finite element space is used for the space discretization and the time discretization is based on an implicit backward Euler method. The a po...

In this exposition, we derive two anisotropic error estimators for parabolic integro-differential equations in a two-dimensional convex polygonal domain. A continuous, piecewise linear finite element space is employed for the space discretization and the time discretization is based on the Crank- Nicolson method. The a posteriori contributions corr...

We derive a posteriori error estimates for both semidiscrete and implicit fully discrete backward Euler method for linear parabolic integro-differential
equations in a bounded convex polygonal or polyhedral domain. A novel space–time reconstruction operator is introduced, which
is a generalization of the elliptic reconstruction operator [2003, SIAM...

## Questions

Question (1)

Please kindly suggest some good FEM softwares for the numerical solution of both time-dependent and time-independent stochastic PDEs.

## Projects

Project (1)

In this project, we are interested in the efficient numerical solution for one-phase and multi-phase inverse Stefan problems in one and higher dimensions using the meshless method of fundamental solutions. In particular, we are interested in finding the automated choice of the MFS parameters while solving the inverse problems efficiently.