NUMERICAL SOLUTION OF MULTIDIMENSIONAL SPECTRAL FRACTIONAL DIFFUSION PROBLEMS: FROM CAFFARELLI TO BURA Лектор: чл.-кор. Св. Маргенов (ИИКТ-БАН) Час: 15:00 Дата: 23.05.2023 г. Място: Зала 503 на ИМИ-БАН Резюме: Fractional diffusion operators appear naturally in many areas in mathematics, physics, ect. The most important property of the related b.v. problems is that they are nonlocal. Let us consider the fractional power of a self-adjoint elliptic operator introduced through its spectral decomposition. It is also self-adjoint but nonlocal. Advanced numerical methods in this area have been heavily influenced by the pioneering work in differential operator theory by Caffarelli and Silvestre, "An Extension Problem Associated with the Fractional Laplacian", 2007. After discretization, nonlocal problems lead to linear systems with dense matrices. In the multidimensional case and domains with general geometry, […]