Abstract:
"Uncertainty of FEM Solutions Using a Nonlinear Least Squares Fit Method and a Design of Experiments Approach"
This paper investigates methods to quantify uncertainty in Finite Element Method (FEM) simulations, specifically focusing on those conducted using COMSOL. The sources of uncertainty addressed are categorized into two main types: mesh-induced truncation errors and uncertainties arising from model parameters. To estimate these, two distinct statistical approaches are employed. For mesh-induced errors, a nonlinear least squares fit method incorporating a 4-parameter logistic distribution is utilized. This method allows for the extrapolation of simulation results to an asymptotic value, providing a "best estimate" of the solution in the limit of infinitely fine meshes, along with an associated confidence interval. For model parameter uncertainties, a Design of Experiments (DOE) approach is adopted. This systematic methodology enables the efficient exploration of the parameter space, helping to identify the most influential parameters and quantify their impact on the simulation outputs. The effectiveness of these methods is demonstrated through practical examples. These include a stress analysis of a wrench using COMSOL's Structural Mechanics module and an application to an MRI RF coil design within the COMSOL RF module. The paper also discusses the application of these techniques with other general-purpose FEM software packages, highlighting the broad applicability of the proposed methodologies. Finally, the significance and limitations of both the nonlinear least squares logistic fit method and the Design of Experiments approach are thoroughly presented and discussed, providing a comprehensive understanding of their utility in enhancing the reliability and accuracy of FEM solutions.
