The collocation and meshless methods for differential equations in R(2)

In recent years, meshless methods have become popular ones to solve differential equations. In this thesis, we aim at solving differential equations by using Radial Basis Functions, collocation methods and fundamental solutions (MFS). These methods are meshless, easy to understand, and even easier to implement

Solving moving-boundary problems with the wavelet adaptive radial basis functions method

Moving boundaries are associated with the time-dependent problems where the momentary position of boundaries needs to be determined as a function of time. The level set method has become an effective tool for tracking, modelling and simulating the motion of free boundaries in fluid mechanics, computer animation and image processing. This work extends our earlier work on solving moving boundary problems with adaptive meshless methods. In particular, the objective of this paper is to investigate numerical performance the radial basis functions (RBFs) methods, with compactly supported basis and with global basis, coupled with a wavelet node refinement technique and a greedy trial space selection technique. Numerical simulations are provided to verify the effectiveness and robustness of RBFs methods with different adaptive techniques

The method of fundamental solutions for solving wave equations

In recent years, the method of fundamental solutions (MFS) has emerged as a novel meshless method in the scientific computing community. In the past, the MFS was essentially restricted to solving homogeneous elliptic equations. Recently, the MFS has gradually extended to solving various types of elliptic and time-dependent problems through the uses of radial basis functions (RBFs); In this thesis, we focus on solving wave equations through the MFS. Currently, there are two major approaches to solve the wave equation: (i) elimination of the time dependence by using the Laplace transform and (ii) discretization in time to approximate the time derivative. We propose to reduce the given wave equations to a series of inhomogeneous modified Helmholtz equations. The solution can then be split into evaluating both homogeneous and particular solutions. To evaluate the homogeneous solution, the MFS is adopted. Furthermore, a closed form particular solution is required for the proposed method. Intensive numerical tests are performed to compare the advantages and disadvantages of these two approaches

A Lagrangian-Eulerian simulation method for viscoelastic flows applied to adhesive joining

Viscoelastic flows are important for many industrial processes, such as adhesive joining, polymer extrusion and additive manufacturing. Numerical simulations enable virtual evaluation and product realization, which can support the design phase and reduce the amount of costly physical testing. However, such applications are challenging to simulate. Thus, efficient, robust and user-friendly simulation methods are needed. In this thesis, a Lagrangian--Eulerian simulation framework for viscoelastic flow is presented. The constitutive equation is solved at Lagrangian nodes, convected by the flow, while the momentum and continuity equations are discretized with the finite volume method. The volume of fluid method is used to model free-surface flow, with an injection model for extrusion along arbitrary nozzle paths. The solver combines an automatic and adaptive octree background grid with implicit immersed boundary conditions. In contrast to boundary-conformed mesh techniques, the framework handles arbitrary geometry and moving objects efficiently. Furthermore, novel coupling methods between the Lagrangian and Eulerian solutions as well as unique treatment of the Lagrangian stresses at the fluid-fluid interface are developed. Consequently, the resulting method can simulate the complex flows associated with the intended applications, without the need for advanced stabilization techniques. The framework is validated for a variety of flows, including relevant benchmarks as well as industrial adhesive joining applications. The latter includes robot-carried adhesive extrusion onto a car fender as well as a hemming application. The results agree with the available experimental data. As such, the research presented in this thesis can contribute to enable virtual process development for joining applications

Chiller Load Forecasting Using Hyper-Gaussian Nets

Energy load forecasting for optimization of chiller operation is a topic that has been receiving increasing attention in recent years. From an engineering perspective, the methodology for designing and deploying a forecasting system for chiller operation should take into account several issues regarding prediction horizon, available data, selection of variables, model selection and adaptation. In this paper these issues are parsed to develop a neural forecaster. The method combines previous ideas such as basis expansions and local models. In particular, hyper-gaussians are proposed to provide spatial support (in input space) to models that can use auto-regressive, exogenous and past errors as variables, constituting thus a particular case of NARMAX modelling. Tests using real data from different world locations are given showing the expected performance of the proposal with respect to the objectives and allowing a comparison with other approaches.Unión Europea RTI2018-101897-B-I00Ministerio de Ciencia e Innovación RTI2018-101897-B-I0