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This paper gives an overview of the use of Polynomial Chaos expansions to represent stochastic processes in numerical simulations. Several methods are presented to perform arithmetic on, as well as to evaluate polynomial and non-polynomial functions of variables respresented with Polynomial Chaos expansions. These methods include Taylor series, a newly… (More)

A rapid approach to monitor ablative therapy through optimizing shape and elasticity parameters is introduced. Our motivating clinical application is targeting and intraoperative monitoring of hepatic tumor thermal ablation, but the method translates to the generic problem of encapsulated stiff masses (solid organs, tumors, ablated lesions, etc.) in… (More)

ecently, interest has grown in developing efficient computational methods (both sampling and nonsampling) for studying ordinary or partial differential equations (ODEs or PDEs) with random inputs. Stochastic Galerkin (SG) methods based on generalized polynomial chaos (gPC) representations have several appealing features (see the sidebar). However, when the… (More)

A maximum entropy (MaxEnt) based probabilistic approach is developed to model mechanical systems characterized by symmetric positive-definite matrices bounded from below and above. These matrices are typically encountered in the constitutive modeling of heterogeneous materials, where the bounds are deduced by employing the principles of minimum… (More)