Theory and Computation of PDE Team

Manoochehr Khasi

Thursday, September 17, 2026 3:00 PM - 4:00 PM

A3-4-312

Zoom 638 227 8222 (BIMSA)

When discretizing a high-dimensional PDE by computational methods, the resulting discretization is a fully discrete scheme. By employing the Kronecker product, the resulting scheme can be formulated as a sparse linear system. For high-dimensional equations, this approach requires a lot of memory, and its computational complexity can increase significantly. Another approach for dealing with these computational challenges is the extended eigenvalue decomposition. This approach constructs a multidimensional operator by exploiting an eigendecomposition of the one-dimensional operator. Applying this operator on the fully discrete scheme, the resulting system is transformed into a diagonal system. Employing the extended eigenvalue decomposition approach for this model reduces the computational complexity and memory requirements and provides an explicit formula for solving the fully discrete scheme.

Dr. Manoochehr Khasi is a researcher at the Iran University of Science and Technology (IUST). His current research interests include spectral methods, meshfree methods, financial mathematics, deep learning, and fractional differential equations. He received his Ph.D. in Numerical Analysis from IUST in 2017 under the supervision of Prof. Rashidinia, where his doctoral research focused on stability improvement of meshfree methods. He was also a postdoctoral researcher at IUST, where his research focused on solving financial models using stable numerical methods.