![]() ![]() ![]() Nevertheless, meshfree methods have recently yielded promising results in the solution of applied problems concerning solidification, inelastic flow in materials forming, mold filling, additive manufacturing, contaminant transport, flow in deformable porous media, and many others. Despite the positive features of meshfree methods, the implementation of such novel numerical techniques for process simulation in realistic applied problems has not yet reached its full potential, much less in the optimal control of these problems. Such difficulties include moving boundaries, large deformations, material discontinuities, complex geometries, and marked gradients. Such methods have made it possible to easily overcome several difficulties that can arise in computational mechanics, for which the solution can be quite cumbersome within the framework of conventional mesh-based techniques. Meshfree methods are numerical techniques entirely based on a set of nodes without any prescribed connectivity to represent the domain in problems governed by partial differential equations. These alternative methods are currently under continuous development, not solely for a more realistic prediction of forward process simulation, but also to effectively address related optimization problems. ![]() The emergence of novel numerical techniques known as meshfree methods has given rise to unprecedented possibilities concerning the accurate capture of relevant physical aspects related to the solution of such mathematical models. A wide range of applied problems are commonly modeled by a system of PDEs, including complex phenomena such as fluid-structure interaction, free-surface flows, phase-change, non-linear thermo-mechanics, large deformations, and material discontinuities. ![]() Mathematical modeling and optimization are important and useful tools for a better understanding of realistic and applied problems commonly modeled by partial differential equations (PDEs), and which have also been found to be particularly helpful in the prediction of industrial process performance and the efficient development of advanced manufacturing technologies. ![]()
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