Announcement Detail
Friday, April 3, 2026
10:00 AM EDT
Join via Zoom: https://utah.zoom.us/j/
Novel Methods Virtual Seminar
Advances in Peridynamics for Modern
Speaker
Selda Oterkus, University of Strathclyde
Abstract:
Peridynamics, a nonlocal reformulation of continuum mechanics, has emerged as a powerful framework for modeling complex material behavior, especially where classical theories face limitations. Its integral-based formulation naturally accommodates discontinuities such as cracks, fragmentation, and multi-physics interactions, enabling more realistic simulation of structural response under extreme loading conditions. Recent advances in numerical schemes, computational efficiency, multiscale coupling, and material model development have significantly broadened the applicability of peridynamics across modern engineering fields.
In this webinar, various applications of peridynamics for
Bio:
Selda Oterkus is a professor in the Department of Naval Architecture, Ocean and Marine Engineering at University of Strathclyde. She is also the Director of PeriDynamics Research Centre and Ocean Energy Research Unit. Her research mainly focuses on multi-physics modelling of materials and structures including damage prediction due to various loading and environmental conditions. Her expertise spans a wide range of topics including fluid-structure interactions, ice-structure interactions, structural health monitoring, digital twin, ships and offshore structures, ship collision, offshore renewable energy, floating wind and solar energy systems, fire damage prediction in composites, corrosion damage, hydrogen embrittlement, and desalination and water treatment technologies. Professor Oterkus was a visiting professor at Stanford University (USA), University of Padova (Italy) and Otto von Guericke University (Germany). She served as a Special Issue Editor for Computational Material Science (Elsevier) and Journal of Mechanics (Cambridge). She is an associate editor of Frontiers in Materials (Frontiers). She is a member of the editorial boards of Scientific Reports (Nature), Journal of Peridynamics and Nonlocal Modeling (Springer), Journal of Marine Science and Engineering (MDPI), and Sustainable Marine Structures (NASS). Additionally, she has served as Chair of ASME UK Section.
A high-order numerical method with unfitted meshes for PDEs on Irregular Domains and Interfaces. Comparison with FEM.
Speaker
Alexander Idesman, Texas Tech University
Abstract:
We present the optimal local truncation error method (OLTEM) for PDEs (e.g., see [1-3]). Similar to the finite difference method, the structure and the width of discrete equations are assumed. The unknown coefficients of the discrete system are calculated by minimization of the order of the local truncation error. The boundary and interface conditions on irregular geometry are imposed as constraints without the introduction of unknowns on boundaries and interfaces. OLTEM provides an optimal high accuracy of discrete equations on trivial unfitted Cartesian meshes (no need in complicated mesh generators) for irregular domains and interfaces (composite materials). OLTEM rigorously calculates the lumped mass matrix for time dependent PDEs. A new OLTEM post-processing procedure for the calculation of the spatial derivatives (e.g., stresses or heat fluxes) that is based on the use of original PDEs significantly increases the accuracy of the spatial derivatives (it is also applicable to FEMand other techniques). For example, 9-th order of accuracy for stresses is obtained by OLTEM with ‘quadratic elements’ for elastostatics [2]. Currently, OLTEM has been applied to the solution of the wave, heat, elastodynamics, Helmholtz, Poisson, Stoke’s and elastostatics equations. The theoretical and numerical results show that at the computational costs of linear finite elements, OLTEM yields the 4th order of accuracy for the considered scalar PDEs on irregular domains and interfaces. At the computational costs of quadratic finite elements, OLTEM yields 10th order of accuracy for elastostatics and 11th order of accuracy for the Poisson equation with complex irregular interfaces (see [1,2]), i.e., the increase in accuracy by 7 and 8 orders compared to FEM. OLTEM reduces the computation time by a factor of 103 - 106 and more [1-3] compared to existing methods and will be effective for the solution of PDEs with stationary and evolving geometry (e.g., crack propagation) on stationary unfitted meshes. We are also working on OLTEM for thin-walled structures.
[1] Idesman A. V., Optimal Local Truncation Error Method for Solution of Partial Differential Equations on Irregular Domains and Interfaces Using Unfitted Cartesian Meshes: Review, Archives of Computational Methods in Engineering, 2023 30, 4517–4564.
[2] Idesman, A., Mobin M., Bishop J., 10-th order of accuracy for numerical solution of 3-D elasticity equations for heterogeneous materials on unfitted Cartesian meshes. Computational Mechanics, 2025, 76, pp. 1085–1115.
[3] Idesman, A., Ajwad, W., Mobin M., Optimal local truncation
Bio:
Dr. Idesman is a Professor in the Department of Mechanical Engineering at Texas Tech University. His research