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Localized collocation schemes and their applications
This paper presents a summary of various localized collocation schemes and their engineering applications. The basic concepts of localized...
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Enhancing PINNs for solving PDEs via adaptive collocation point movement and adaptive loss weighting
Physics-informed neural networks (PINNs) are an emerging method for solving partial differential equations (PDEs) and have been widely applied in the...
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Solution of Fractional Optimal Control Problems by using orthogonal collocation and Multi-objective Optimization Stochastic Fractal Search
In this contribution the solution of Fractional Optimal Control Problems (FOCP) by using the Orthogonal Collocation Method (OCM) and the...
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Stochastic finite element analysis using polynomial chaos on a flexible rotor with contact nonlinearity
The dynamic response of a rotor system can be significantly affected by uncertainties. It is essential to understand and quantify the influence of...
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Collocation Methods and Beyond in Non-linear Mechanics
Within the realm of isogeometric analysis, isogeometric collocation has been driven by the attempt to minimize the cost of quadrature associated with...
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Efficient approximation of stochastic turning process based on power spectral density
Turning is one of the most important material removal processes in manufacturing, where the proper understanding of the process is crucial for the...
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Stochastic uncertain lubrication in gear transmission subjected to tribodynamic loading
A stochastic uncertain tribodynamic model is established for a spur gear pair for the first time. The stochastic uncertainty of pinion rotation speed...
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Stochastic virtual element methods for uncertainty propagation of stochastic linear elasticity
This paper presents stochastic virtual element methods for propagating uncertainty in linear elastic stochastic problems. We first derive stochastic...
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Efficient and accurate uncertainty quantification in engineering simulations using time-separated stochastic mechanics
A robust method for uncertainty quantification is undeniably leading to a greater certainty in simulation results and more sustainable designs. The...
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Approximating a New Class of Stochastic Differential Equations via Operational Matrices of Bernoulli Polynomials
In the current paper, we introduce an efficient methodology to solve nonlinear stochastic differential equations (SDEs) driven by variable order...
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A Comparison of Matrix-Free Isogeometric Galerkin and Collocation Methods for Karhunen–Loève Expansion
Numerical computation of the Karhunen–Loève expansion is computationally challenging in terms of both memory requirements and computing time. We...
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On Multilevel RBF Collocation Based on Operator Newton Iteration to Solve Nonlinear Black–Scholes Equations
Nonlinear partial differential equations are now playing an increasingly important role in the modeling of financial markets. In this paper, we...
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A new paradigm for the efficient inclusion of stochasticity in engineering simulations: Time-separated stochastic mechanics
As a physical fact, randomness is an inherent and ineliminable aspect in all physical measurements and engineering production. As a consequence,...
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Meshless Barycentric Rational Interpolation Method for Solving Nonlinear Stochastic Fractional Integro-Differential Equations
This article suggests an accurate computational approach based on meshless barycentric rational interpolation and spectral method to solve a class of...
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A Review of Stochastic Analysis of the Seepage Through Earth Dams with a Focus on the Application of Monte Carlo Simulation
The purpose of this paper is a comprehensive literature review of different aspects of seepage analysis of earth-fill and rock-fill dams, emphasizing...
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A machine learning method for computing quasi-potential of stochastic dynamical systems
The concept of quasi-potential plays a central role in understanding the mechanisms of rare events and characterizing the statistics of transition...
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Spectral projection and linear regression approaches for stochastic flexural and vibration analysis of laminated composite beams
This paper presents a novel approach for assessing the uncertainty in vibration and static responses of laminated composite beams resulting from...
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Semi-reduced order stochastic finite element methods for solving contact problems with uncertainties
This paper develops two-step methods for solving contact problems with uncertainties. In the first step, we propose stochastic Lagrangian...
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Global analysis of stochastic and parametric uncertainty in nonlinear dynamical systems: adaptative phase-space discretization strategy, with application to Helmholtz oscillator
An adaptative phase-space discretization strategy for the global analysis of stochastic nonlinear dynamical systems with competing attractors...
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Rapid aerodynamic shape optimization under uncertainty using a stochastic gradient approach
A common approach in aerodynamic design is to optimize a performance function—provided some constraints—defined by a choice of an aerodynamic model...
