3 papers
math.OC2026
Generalized Adjoint Method
Andrew Zheng, Adam R. Stinchcombe
The adjoint method is an efficient way to numerically compute gradients in optimization problems with constraints, but is only formulated to differentiable cost and constraint func…
math.NA2025
Evaluating singular and near-singular integrals on smooth surfaces with quadratic geometric approximation and closed form expressions
Andrew Zheng, Spyros Alexakis, Adam R Stinchcombe
Most Fredholm integral equations involve integrals with weakly singular kernels. Once the domain of integration is discretized into flat triangular elements, these weakly singular…
math.NA2025
Walk-on-Interfaces: A Monte Carlo Estimator for an Elliptic Interface Problem with Nonhomogeneous Flux Jump Conditions and a Neumann Boundary Condition
Xinwen Ding, Adam R Stinchcombe
Elliptic interface problems arise in numerous scientific and engineering applications, modeling heterogeneous materials in which physical properties change discontinuously across i…