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Utkarsh Rajput

Publications and source records attributed to Utkarsh Rajput.

3 recordsLinked to original sources

A virtual element method for Kelvin--Voigt viscoelasticity

Considering the computational advantages of virtual element methods (VEM), this work employs a conforming VEM for the numerical approximation of the Kelvin--Voigt model of viscoelasticity. For clarity and simplicity, we focus on the primal formulation. The spatial discretization is carried out using the virtual element method, while the temporal discretization is handled via the {second-order Crank--Nicolson} scheme. We establish the well-posedness of both the semi-discrete and fully discrete problems and derive {\it a priori} error estimates. Several representative numerical examples are presented to validate the theoretical results and to demonstrate the effectiveness of the proposed formulation.

math.NA

Mixed virtual element methods for a stress-velocity-rotation formulation in viscoelasticity

In this paper we propose a new mixed virtual element formulation for the numerical approximation of viscoelasticity equations with weakly imposed stress symmetry. The governing equations use the Zener model and are expressed in terms of the principal unknowns of additively decomposed stress into elastic and internal viscoelastic contributions, while the rotation tensor and velocity act as Lagrange multipliers. The time discretisation uses Crank--Nicolson's scheme. We demonstrate the unique solvability of both semi-discrete and fully-discrete problems by leveraging the properties of suitable local projectors. Moreover, we establish optimal a priori error estimates for all variables that appear in the mixed formulation. To validate our theoretical findings, we present several representative numerical examples that also highlight the features of the proposed formulation.

math.NA

Composing Modeling and Simulation with Machine Learning in Julia

In this paper we introduce JuliaSim, a high-performance programming environment designed to blend traditional modeling and simulation with machine learning. JuliaSim can build accelerated surrogates from component-based models, such as those conforming to the FMI standard, using continuous-time echo state networks (CTESN). The foundation of this environment, ModelingToolkit.jl, is an acausal modeling language which can compose the trained surrogates as components within its staged compilation process. As a complementary factor we present the JuliaSim model library, a standard library with differential-algebraic equations and pre-trained surrogates, which can be composed using the modeling system for design, optimization, and control. We demonstrate the effectiveness of the surrogate-accelerated modeling and simulation approach on HVAC dynamics by showing that the CTESN surrogates accurately capture the dynamics of a HVAC cycle at less than 4\% error while accelerating its simulation by 340x. We illustrate the use of surrogate acceleration in the design process via global optimization of simulation parameters using the embedded surrogate, yielding a speedup of two orders of magnitude to find the optimum. We showcase the surrogate deployed in a co-simulation loop, as a drop-in replacement for one of the coupled FMUs, allowing engineers to effectively explore the design space of a coupled system. Together this demonstrates a workflow for automating the integration of machine learning techniques into traditional modeling and simulation processes.

cs.CE