2022/02/05 by Jie Liu, Henk M. Schuttelaars, Liu, Jie +3
Engineering · Physics and Astronomy · #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.2202.02572
openalex publication_date 2022/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using the standard finite element method (FEM) to solve general partial differential equations, the round-off error is found to be proportional to N^β\rm R, with N the number of degrees of freedom (DoFs) and β\rm R a coefficient. A method which uses a few cheap numerical experiments is proposed to determine the coefficient of proportionality and β\rm R in various space dimensions and FEM packages. Using the coefficients obtained above, the strategy put forward in \citeliu386balancing for predicting the highest achievable accuracy E\rm min and the associated optimal number of DoFs N\rm opt for specific problems is extended to general problems. This strategy allows predicting E\rm min accurately for general problems, with the CPU time for obtaining the solution with the highest accuracy E\rm min typically reduced by 60%--90%.