In geophysical applications direct current (DC) resistivity surveys are collected by injecting current and recording voltage potentials over a field site of interest. These data sets can provide valuable non-invasive images of the sub-surface. The optimization problem that arrises in producing these images requires multiple solves of a linear system with numerous right hand sides (RHSs). Due to...

In this work, we investigate a particular class of shape optimization problems under uncertainties on the input parameters. More precisely, we are interested in the minimization of the expectation of a quadratic objective in a situation where the state function depends linearly on a random input parameter. This framework covers important objectives such as tracking-type functionals for elliptic...

A new a posteriori error estimator is presented for the verification of the dimensionally reduced models stemming from the elliptic problems on thin domains. The original problem is considered in a general setting, without any specific assumptions on the domain geometry, coefficients, and the right-hand sides. For the energy norm of the error of the zero-order dimension reduction method, the pr...

In this paper we identify systems of an arbitrary number $$N$$ first-order Ordinary Differential Equations with nonlinear homogeneous right-hand sides (integer, positive or nonpositive) degree $$M$$ , which feature very simple explicit solutions; as well variants these systems—with no more homogeneous—some periodic solutions. A novelty findings is to consider characterized by constraints involv...

Block Toeplitz matrices are a special class of that exhibit reduced memory requirements and complexity matrix-vector multiplications. We herein present an efficient computational approach to solve sequence block systems arising from system with multiple right-hand sides. Two different numerical schemes implemented for the solution based on global variants generalized minimal residual (GMRES) me...

in this paper an optimal controller is proposed for a self-balancing electrical vehicle called segway pt. this vehicle has one platform and two wheels on the sides and the rider stands on the platform. a handlebar, as a navigator, is attached to the body of segway, with which the rider controls the vehicle. since segway uses electrical energy produced by batteries, resource consumption manageme...

We introduce a family of first-order multidimensional ordinary differential equations (ODEs) with discontinuous right-hand sides and demonstrate their applicability in image processing. An equation belonging to this family is an inverse diffusion everywhere except at local extrema, where some stabilization is introduced. For this reason, we call these equations "stabilized inverse diffusion equ...