This article presents a general and novel approach to the automation of goal-oriented error control in the solution of nonlinear stationary finite element variational problems. The approach is based on automated linearization to obtain the linearized dual problem, automated derivation and evaluation of a posteriori error estimates, and automated adaptive mesh refinement to control the error in ...

We proposed a general formulation of the successive linearization method for solving highly nonlinear boundary value problem arising in rotating disk flow. The problem was studied under the effects of partial slip, thermal diffusion, and diffusion-thermo. The governing fundamental conservation equations of mass, momentum, angular momentum, energy, and concentration are transformed into a system...

The Quadratic Arnoldi algorithm is an Arnoldi algorithm for the solution of the quadratic eigenvalue problem, that exploits the structure of the Krylov vectors. This allows us to reduce the memory requirements by about a half. The method is an alternative to the Second Order Arnoldi method (SOAR). In the SOAR method it is not clear how to perform an implicit restart. We discuss various choices ...

We present a new approach to the optimization of plasma scenarios in tokamaks. We formulate this task as an optimal control problem and use numerical methods for optimization problems with partial differential equation (PDE) constraints. The latter are discretized by linear finite elements and implicit Euler time stepping. Due to the free-boundary setting, we have introduced a new linearization...

We describe a compactification by KSBA stable pairs of the five-dimensional moduli space K3 surfaces with purely non-symplectic automorphism order four and $U(2)\oplus D_4^{\oplus 2}$ lattice polarization. These can be realized as minimal resolution double cover $\mathbb {P}^{1}\times \mathbb {P}^{1}$ branched along specific $(4,\,4)$ curve. show that, up to finite group action, this is isomorp...

Nonlinear coupled partial differential equations are physical problems since it makes the unnecessary very important in a variety of scientific fields. They arise linearization, perturbation problem being solved. in large number of mathematical and engineering In this study, the ADM is extended to problems, especially in fluid mechanics, solid state analytic-numeric simulation for strictly hype...

This paper compares and discusses four techniques for model order reduction based on compressed sensing (CS), less relevant basis removal (LRBR), principal component analysis (PCA) and partial least squares (PLS). CS and PCA have already been used for reducing the order of power amplifier (PA) behavioral models for digital predistortion (DPD) purposes. While PLS, despite being popular in some s...

discretized with first order finite volume schemes. This problem is representative of many transport problems, such as transfer and neutron transport, for which the small parameter ε is the ratio of two very different sound velocities and σ is the absorption or the opacity. For simplicity both ε and σ > 0 are kept constant in space in this study. The system (1.1) can also be introduced as a spe...

We develop partial differential equation (PDE) methods to study the dynamics of pattern formation in partial integro-differential equations (PIDEs) defined on a spatially extended domain. Our primary focus is on scalar equations in two spatial dimensions. These models arise in a variety of neuronal modeling problems and also occur in material science. We first derive a PDE which is equivalent t...