Speaker: Boyan Lazarov, Lawrence Livermore National Laboratory

Time : 16:00 - 17:00 CEST (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

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Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords: Random field generation; Topology optimization; Stochastic optimization

Abstract: Fractional stochastic partial differential equations (SPDEs) provide a flexible framework for modeling spatial uncertainty in computational mechanics. By linking fractional elliptic operators to Matérn-type Gaussian random fields, they allow systematic control of field smoothness, correlation length, and anisotropy on complex geometries and embedded surfaces.

This talk focuses on the formulation and finite element approximation of these fractional SPDEs. We discuss how fractional powers of elliptic operators transform spatial white noise into correlated random fields, and how rational approximations enable their numerical treatment through a sequence of standard elliptic solves. Together with efficient finite element white noise sampling, this approach supports scalable random field generation directly on the mesh used for the physical simulation. Its implementation in the open-source library MFEM provides a practical connection between fractional operators and uncertainty quantification workflows.

Applications to geometric uncertainty in cerebral aneurysms and topology optimization of thermal and structural systems demonstrate the framework’s versatility. These examples show how spatial correlation and anisotropy influence predicted responses and optimized designs, highlighting fractional SPDEs as a computationally accessible foundation for incorporating spatial uncertainty into simulation and optimization.

Biography: Boyan Lazarov is a Research Engineer in the Computational Engineering Division at Lawrence Livermore National Laboratory (LLNL). His work centers on methods and tools for modeling, design, and optimization of coupled multiphysics systems at scale, leveraging high-performance computing. Application areas span fluid–thermal systems, photonics, acoustics, and structural/mechanical design for the automotive and aerospace industries. Before joining LLNL in 2019, he was a Senior Lecturer in Mechanical and Aerospace Engineering at the University of Manchester (UK) and a Senior Scientist at the Technical University of Denmark (DTU). He has also held visiting scholar and industrial engineering roles in the US, UK, and Germany. Dr. Lazarov earned his Ph.D. in Mechanical Engineering from DTU and has authored more than 60 peer-reviewed journal papers. He has developed and contributed to multiple closed- and open-source finite-element and topology-optimization software libraries.

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