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Key research themes
1. How can encapsulated error arithmetic improve floating-point numerical accuracy assessment in large-scale simulations?
This research theme focuses on developing new arithmetic methods that directly estimate and track numerical errors arising from floating-point operations. The goal is to achieve accurate, low-overhead, and scalable error quantification that can be integrated into complex numerical applications, including parallel and mixed-precision computations. Traditional methods often rely on high-precision computations or static verifications, which are costly or limited in scope. Encapsulated error arithmetic encapsulates both computed result and its error approximation, enabling precise measurement of significant digits dynamically across all intermediate results in a numerical simulation.
Key finding: Introduces 'Encapsulated error', a direct method encapsulating both the floating-point result and its numerical error approximation in a dedicated arithmetic type. The approach enables measurement of significant digits at all... Read more
Key finding: Presents a refined implementation and detailed evaluation of encapsulated error arithmetic, validating its effectiveness for floating-point accuracy estimation in large computations. The method’s key contribution lies in... Read more
Key finding: Details an implementation of significance arithmetic in Mathematica that dynamically adjusts computational precision and tracks error propagation in floating-point calculations. Unlike fixed-precision IEEE 754 arithmetic,... Read more
2. What statistical and computational methodologies enable accurate and efficient error estimation in measurement and coordinate metrology?
This theme addresses the quantification and estimation of measurement uncertainty, accuracy, and maximum permissible error (MPE) in metrology systems, combining traditional statistical approaches with novel computational techniques such as Monte Carlo simulations and streamlined sampling strategies. The focus is on ensuring confidence in performance verification of measurement instruments, minimizing data collection overhead, and addressing error components including systematic and environmental factors. The approaches include empirical, simulation-based, and hybrid methods applicable across disciplines requiring precise coordinate or geometric measurements.
Key finding: Demonstrates the efficacy of Monte Carlo (MC) simulations as a universal and intuitive tool for estimating both individual and combined components of measurement uncertainty. Shows that MC facilitates direct empirical... Read more
Key finding: Proposes a novel statistical method to estimate maximum permissible errors (MPEs) from minimal repeat measurements with high confidence, addressing limitations of naive maximum error approaches. The method achieves close... Read more
Key finding: Develops FPGA streaming reduction circuits enhanced with compensated summation techniques to improve numerical accuracy of floating-point accumulations critical in metrology and scientific computations. Experimental results... Read more
3. How does mesh skewness affect numerical stability and accuracy in finite-difference schemes for solving partial differential equations?
This research theme investigates the influence of non-orthogonal, skewed computational meshes on the stability and accuracy of finite-difference discretizations, particularly for advection-diffusion problems and related numerical methods applied to fluid flow and large-eddy simulations. Numerical instability arising from mesh skewness may lead to significant phase errors, amplitude damping, and stringent timestep constraints. Understanding these effects is vital for mesh design, error control, and the development of stable and accurate solution algorithms for complex geometries where skewed meshes are unavoidable.
Key finding: Conducts a comprehensive truncation error and modified wavenumber analysis on transformed advection-diffusion equations discretized with central and upwind finite-difference schemes. Shows that severe mesh skewness amplifies... Read more