Test-Driven Development of a Substructuring Technique for the Analysis of Electromagnetic Finite Periodic Structures

In this paper, we follow the Test-Driven Development (TDD) paradigm in the development of an in-house code to allow for the finite element analysis of finite periodic type electromagnetic structures (e.g., antenna arrays, metamaterials, and several relevant electromagnetic problems). We use unit and integration tests, system tests (using the Method of Manufactured Solutions—MMS), and application tests (smoke, performance, and validation tests) to increase the reliability of the code and to shorten its development cycle. We apply substructuring techniques based on the definition of a unit cell to benefit from the repeatability of the problem and speed up the computations. Specifically, we propose an approach to model the problem using only one type of Schur complement which has advantages concerning other substructuring techniques.

Rapid Response! Investigating the Effects of Problem Definition on the Characteristics of Additively Manufactured Solutions for COVID-19

Designers from around the world have proposed numerous engineering design solutions for problems related to the COVID-19 pandemic, many of which leverage the rapid prototyping and manufacturing capabilities of additive manufacturing (AM). While some of these solutions are motivated by complex and urgent requirements (e.g., face masks), others are motivated by simpler and less urgent needs (e.g., hands-free door openers). Previous research suggests that problem definition influences the creativity of solutions generated for it. In this study, we investigate the relationship between the definition of problems related to the COVID-19 pandemic and the characteristics of AM solutions that were openly shared for these problems. Specifically, we analyze 26 AM solutions spanning three categories: (1) hands-free door openers (low complexity problem), (2) face shields (moderate complexity problem), and (3) face masks (high complexity problem). These designs were compared on (1) DfAM utilization, (2) manufacturability (i.e., build time, cost, and material usage), and (3) creativity. We see that the solutions designed for the high complexity problem, i.e., face masks, were least suitable for AM. Moreover, we see that solutions designed for the moderate complexity problem, i.e., face shields, had the lowest build time, build cost, and material consumption. Finally, we observe that the problem definition did not relate to the creativity of the AM solutions. In light of these findings, designers must sufficiently emphasize the AM suitability and manufacturability of their solutions when designing for urgent and complex problems in rapid response situations.

Adaptive Semi-Structured Mesh Refinement Techniques for the Finite Element Method

The adaptive mesh techniques applied to the Finite Element Method have continuously been an active research line. However, these techniques are usually applied to tetrahedra. Here, we use the triangular prismatic element as the discretization shape for a Finite Element Method code with adaptivity. The adaptive process consists of three steps: error estimation, marking, and refinement. We adapt techniques already applied for other shapes to the triangular prisms, showing the differences here in detail. We use five different marking strategies, comparing the results obtained with different parameters. We adapt these strategies to a conformation process necessary to avoid hanging nodes in the resulting mesh. We have also applied two special rules to ensure the quality of the refined mesh. We show the effect of these rules with the Method of Manufactured Solutions and numerical results to validate the implementation introduced.

The Performance of a Gradient-Based Method to Estimate the Discretization Error in Computational Fluid Dynamics

Although the grid convergence index is a widely used for the estimation of discretization error in computational fluid dynamics, it still has some problems. These problems are mainly rooted in the usage of the order of a convergence variable within the model which is a fundamental variable that the model is built upon. To improve the model, a new perspective must be taken. By analyzing the behavior of the gradient within simulation data, a gradient-based model was created. The performance of this model is tested on its accuracy, precision, and how it will affect a computational time of a simulation. The testing is conducted on a dataset of 36 simulated variables, simulated using the method of manufactured solutions, with an average of 26.5 meshes/case. The result shows the new gradient based method is more accurate and more precise then the grid convergence index(GCI). This allows for the usage of a coarser mesh for its analysis, thus it has the potential to reduce the overall computational by at least by 25% and also makes the discretization error analysis more available for general usage.