2015/11/09 by Jürgen Dölz, Helmut Harbrecht, Dölz, Jürgen +4
Decision Sciences · Engineering · Physics and Astronomy · #60H35 #65C30 #65N30 #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Scattering and Analysis #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.1511.02626
openalex publication_date 2015/11/09 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
We consider the efficient solution of strongly elliptic partial differential\nequations with random load based on the finite element method. The solution's\ntwo-point correlation can efficiently be approximated by means of an\n\H-matrix, in particular if the correlation length is rather short\nor the correlation kernel is non-smooth. Since the inverses of the finite\nelement matrices which correspond to the differential operator under\nconsideration can likewise efficiently be approximated in the\n\H-matrix format, we can solve the correspondent\n\H-matrix equation in essentially linear time by using the\n\H-matrix arithmetic. Numerical experiments for three-dimensional\nfinite element discretizations for several correlation lengths and different\nsmoothness are provided. They validate the presented method and demonstrate\nthat the computation times do not increase for non-smooth or shortly correlated\ndata.\n