In engineering sciences, we classify mathematical models as ‘proper’ or ‘improper’ rather than ‘scientific’ or ‘pseudoscientific’. A model is said to be proper if it is consistent with the relevant mathematical theorems that guarantee the existence and, when applicable, the uniqueness of the exact solution. Otherwise, the model is improper. At present, the large majority of models used in engineering practice are improper. Following are examples of frequently occurring types of error, with brief explanations.
Mathematical models have become indispensable sources of information on which technical and business decisions are based. It is therefore vitally important for decision-makers to know whether relying on the predictions of mathematical models is justified. When properly used, numerical simulation can be a major corporate asset. However, it can become a major corporate liability if the reliability of predictions is not guaranteed. Learn more in our latest blog post.
Smart Engineering Simulation Applications, (SESA or Sim Apps), are software tools crafted by expert analysts to standardize recurring simulation tasks. Learn more about how Sim Apps and AI tools can work together to enhance engineering simulation workflows.
Engineering students and professionals alike want to know: are singularities “real”? And if so, when they appear in our solutions, what are we supposed to do with them?
Regarding the practical question of what to do with singularities; we need to distinguish between cases where singularities are just nuisances and where a singularity is the object of simulation.
From all of us at ESRD, we wish you a very happy holiday season! We truly feel that each and every one of our users are part of the ESRD family and we are incredibly grateful to get to work with all of you.
There is much we are thankful for as we approach the end of the year, and we’d like to take a moment to acknowledge some of the reasons we’re looking back fondly on 2023…
A mathematician delivered a keynote presentation at an engineering conference some years ago. At the coffee break, following the presentation, a highly respected senior developer of a legacy finite element code, remarked: “I do not understand why the speaker was so worried about singularities. We never see them.”
The remark highlights the lack of a common language between the pre-scientific notion of finite element modeling and finite element analysis, which is a branch of applied mathematics. Read why mathematicians and engineers alike should “worry” about singularities.
The idea of achieving convergence by increasing the polynomial degree (p) of the approximating functions on a fixed mesh, known as the p-version of the finite element method, was at odds with the prevailing view in the finite element research community in the 1960s and 70s. But why?
It is generally recognized that explainable artificial intelligence (XAI) will play an important role in numerical simulation where it will impose the requirements of reliability, traceability, and auditability. These requirements will necessitate clear thinking about the nature of mathematical models, the trustworthiness of their predictions, and ways to improve their reliability.
The term “simulation” is often used interchangeably with “finite element modeling” in the engineering literature and marketing materials. It is important to understand the difference between the two.
The development of the finite element method (FEM) consists of two main branches: the art of finite element modeling and the science of finite element analysis. Learn why in this blog.
The software provides a highly reliable and user-friendly production stress analysis tool that will replace the Finite Element Method (FEM) tools and failure criteria the experts currently employ for analyzing bonded joints. The software includes an FEM-based handbook format, which allows non-experts to utilize models prepared by specialists. The handbook problems include built-in failure criteria, geometric and material nonlinearities, and the modern FEM technology provides better error control and the treatment of very large aspect ratios.”
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