Related Experiment Video
Updated: Nov 2, 2025

Planar Gradient Diffusion System to Investigate Chemotaxis in a 3D Collagen Matrix
Published on: June 12, 2015
A stochastic collocation approach for parabolic PDEs with random domain deformations
Julio E Castrillón-Candás1, Jie Xu1
1Boston University, Department of Mathematics and Statistics, 111 Cummington Mall, Boston, MA 02215.
Abstract:
In this article we analyze the linear parabolic partial differential equation with a stochastic domain deformation. In particular, we concentrate on the problem of numerically approximating the statistical moments of a given Quantity of Interest (QoI). The geometry is assumed to be random. The parabolic problem is remapped to a fixed deterministic domain with random coefficients and shown to admit an extension on a well defined region embedded in the complex hyperplane. The stochastic moments of the QoI are computed by employing a collocation method in conjunction with an isotropic Smolyak sparse grid. Theoretical sub-exponential convergence rates as a function to the number of collocation interpolation knots are derived. Numerical experiments are performed and they confirm the theoretical error estimates.
Related Concept Videos
Poisson's And Laplace's Equation
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
Castigliano's Theorem
Divergence and Stokes' Theorems
Second Derivatives and Laplace Operator
Consider a scalar function. The curl of its...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...

