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math.NA2026
Parametric Sensitivity of POD Reduced-Order Models for Semilinear Evolution Equations with Applications to G-Equations
Shengbo Ma, Luhao Xue, Zhiwen Zhang
Proper Orthogonal Decomposition (POD) provides low-dimensional surrogate models of evolution equations from solution snapshots. In parameterized problems, however, a basis computed…
math.NA2026
A Recursive Polynomial Chaos Evolution Method for Stochastic Differential Equations
Guillaume Bal, Shengbo Ma, Su Zhang +1
Numerical simulation of stochastic differential equations over long time intervals poses significant computational challenges. In this paper, we propose a novel recursive polynomia…
math.NA2024
Uncertainty Quantification of Phase Transition Problems with an Injection Boundary
Zhenyi Zhang, Shengbo Ma, Zhennan Zhou
We develop an enthalpy-based modeling and computational framework to quantify uncertainty in Stefan problems with an injection boundary. Inspired by airfoil icing studies, we consi…