In a remarkable display of academic excellence, On May 3, 2023, Yang Liu successfully defended his PhD proposal entitled " Hierarchical sampling techniques and goal-oriented adaptive finite element methods with application to elliptic PDEs with lognormal coefficients.
Committee Chairperson:
Prof. Raúl Tempone, AMCS, KAUST
Committee Members:
Prof. Daniele Boffi, AMCS, KAUST
Prof. David Bolin, AMCS, KAUST
Abstract:
We propose our Adaptive Multilevel Monte Carlo (AMLMC) method to solve an elliptic partial differential equation with lognormal random input data where the PDE model has geometry-induced singularities. This work combines (MLMC) and the dual-weighted-residual goal-oriented adaptive finite element. Specifically, for a given input coefficient realization and an accuracy level, the (AMLMC) constructs its approximate sample as the ones using the first mesh in the sequence of pre-generated, non-uniform meshes satisfying the sample-dependent bias constraint.
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