<oai_dc:dc xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
  <dc:contributor>Krause, Rolf</dc:contributor>
  <dc:contributor>Donatelli, Marco</dc:contributor>
  <dc:creator>Trotti, Ken</dc:creator>
  <dc:date>2021-12-15</dc:date>
  <dc:description xmlns:ns0="xml" ns0:lang="en">Recent years have seen the rapid growth in interest towards fractional calculus. Fractional calculus plays an important role in  modelling anomalous diffusion phenomena, however closed-form analytical solutions of such equations are rarely available, hence  numerical estimates are needed. In this thesis we consider various fractional diffusion equations (FDEs), where different fractional  derivative definitions and related discretizations are involved and we focus on multigrid-based approaches for solving the associated  linear systems. Precisely, we will leverage the spectral properties of the coefficient matrix, retrieved by exploiting its structure, to  design ad-hoc (tailored) multigrid solvers or preconditioners for Krylov methods. We develop a new approach to compute the Jacobi  weight, which is versatile enough to work with various FDEs and allows to build a parameter free multigrid method. Moreover, in the  case of uniform meshes, we exploit the knowledge about anisotropic integer-order partial diffusion equations to deal with anisotropic  FDEs, by building a robust multigrid-based solver. Furthermore, we study the behavior of multigrid methods as parallel-in-time  solvers and, then, we provide a new second-order accurate finite volume approximation and related ad-hoc multigrid solver. Finally,  we extend our multigrid strategies to deal with a singular one-dimensional space-FDE discretized over non-uniform meshes.</dc:description>
  <dc:format>application/pdf</dc:format>
  <dc:identifier>https://susi.usi.ch/global/documents/319220</dc:identifier>
  <dc:identifier>https://localhost:5000/ark:/12658/srd1319220</dc:identifier>
  <dc:identifier>https://susi.usi.ch/documents/319220/files/2021INFO013.pdf</dc:identifier>
  <dc:language>eng</dc:language>
  <dc:relation>info:eu-repo/semantics/altIdentifier/urn/urn:nbn:ch:rero-006-119589</dc:relation>
  <dc:relation>info:eu-repo/semantics/altIdentifier/ark/12658/srd1319220</dc:relation>
  <dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
  <dc:rights>License undefined</dc:rights>
  <dc:subject xmlns:ns1="xml" ns1:lang="en">Multigrid methods</dc:subject>
  <dc:subject xmlns:ns2="xml" ns2:lang="en">Fractional diffusion equations</dc:subject>
  <dc:subject xmlns:ns3="xml" ns3:lang="en">Symbol analysis</dc:subject>
  <dc:subject xmlns:ns4="xml" ns4:lang="en">Toeplitz matrices</dc:subject>
  <dc:subject xmlns:ns5="xml" ns5:lang="en">Structured meshes</dc:subject>
  <dc:subject>info:eu-repo/classification/udc/004</dc:subject>
  <dc:title xmlns:ns6="xml" ns6:lang="en">Multigrid methods for fractional diffusion equations</dc:title>
  <dc:type>http://purl.org/coar/resource_type/c_db06</dc:type>
</oai_dc:dc>