Related papers: Evolutionary Mesh Numbering: Preliminary Results
Evolutionary algorithms are metaheuristic techniques that derive inspiration from the natural process of evolution. They can efficiently solve (generate acceptable quality of solution in reasonable time) complex optimization (NP-Hard)…
Classical and new numerical schemes are generated using evolutionary computing. Differential Evolution is used to find the coefficients of finite difference approximations of function derivatives, and of single and multi-step integration…
We consider problems related to initial meshing and adaptive mesh refinement for the electromagnetic simulation of various structures. The quality of the initial mesh and the performance of the adaptive refinement are of great importance…
Finding optimal solutions to combinatorial optimization problems is pivotal in both scientific and technological domains, within academic research and industrial applications. A considerable amount of effort has been invested in the…
Evolutionary algorithms (EAs) are population-based metaheuristics, originally inspired by aspects of natural evolution. Modern varieties incorporate a broad mixture of search mechanisms, and tend to blend inspiration from nature with…
Estimating the effort of software systems is an essential topic in software engineering, carrying out an estimation process reliably and accurately for a software forms a vital part of the software development phases. Many researchers have…
Initial population plays an important role in heuristic algorithms such as GA as it help to decrease the time those algorithms need to achieve an acceptable result. Furthermore, it may influence the quality of the final answer given by…
We consider a hybrid FEM-BEM method to compute approximations of full-space linear elliptic transmission problems. First, we derive a priori and a posteriori error estimates. Then, building on the latter, we present an adaptive algorithm…
Computational analysis with the finite element method requires geometrically accurate meshes. It is well known that high-order meshes can accurately capture curved surfaces with fewer degrees of freedom in comparison to low-order meshes.…
Tensor networks are a tool first employed in the context of many-body quantum physics that now have a wide range of uses across the computational sciences, from numerical methods to machine learning. Methods integrating tensor networks into…
One of the major issues in the computational mechanics is to take into account the geometrical complexity. To overcome this difficulty and to avoid the expensive mesh generation, geometrically unfitted methods, i.e. the numerical methods…
The Finite Element Method (FEM) is widely used to solve discrete Partial Differential Equations (PDEs) in engineering and graphics applications. The popularity of FEM led to the development of a large family of variants, most of which…
Simulating physical systems is essential in engineering, but analytical solutions are limited to straightforward problems. Consequently, numerical methods like the Finite Element Method (FEM) are widely used. However, the FEM becomes…
Genetic algorithms are modeled after the biological evolutionary processes that use natural selection to select the best species to survive. They are heuristics based and low cost to compute. Genetic algorithms use selection, crossover, and…
We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by…
In this article we provide a comprehensive review of the different evolutionary algorithm techniques used to address multimodal optimization problems, classifying them according to the nature of their approach. On the one hand there are…
The convergence analysis for least-squares finite element methods led to various adaptive mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteriori error estimator or an alternative explicit…
Evolutionary algorithms are good general problem solver but suffer from a lack of domain specific knowledge. However, the problem specific knowledge can be added to evolutionary algorithms by hybridizing. Interestingly, all the elements of…
Bayesian inverse problems are an important application for probabilistic solvers of partial differential equations: when fully resolving numerical error is computationally infeasible, probabilistic solvers can be used to consistently model…
Arnold, Falk, and Winther [Bull. Amer. Math. Soc. 47 (2010), 281--354] showed that mixed variational problems, and their numerical approximation by mixed methods, could be most completely understood using the ideas and tools of Hilbert…