A computational framework is presented to numerically simulate the effects of antihypertensive drugs, in particular calcium channel blockers, on the mechanical response of arterial walls. A stretch-dependent smooth muscle model by Uhlmann and Balzani is modified to describe the interaction of pharmacological drugs and the inhibition of smooth muscle activation. The coupled deformation-diffusion problem is then solved using the finite element software FEDDLib and overlapping Schwarz preconditioners from the Trilinos package FROSch. These preconditioners include highly scalable parallel GDSW (generalized Dryja–Smith–Widlund) and RGDSW (reduced GDSW) preconditioners. Simulation results show the expected increase in the lumen diameter of an idealized artery due to the drug-induced reduction of smooth muscle contraction, as well as a decrease in the rate of arterial contraction in the presence of calcium channel blockers. Strong and weak parallel scalability of the resulting computational implementation are also analyzed.@en

A new reduced-dimension adaptive generalized Dryja-Smith-Widlund (GDSW) overlapping Schwarz method for linear second-order elliptic problems in three dimensions is introduced. It is robust with respect to large contrasts of the coefficients of the partial differential equations. The condition number bound of the new method is shown to be independent of the coefficient contrast and only dependent on a user-prescribed tolerance. The interface of the nonoverlapping domain decomposition is partitioned into nonoverlapping patches. The new coarse space is obtained by selecting a few eigenvectors of certain local eigenproblems which are defined on these patches. These eigenmodes are energy-minimally extended to the interior of the nonoverlapping subdomains and added to the coarse space. By using a new interface decomposition, the reduced-dimension adaptive GDSW overlapping Schwarz method usually has a smaller coarse space than existing GDSW and adaptive GDSW domain decomposition methods. A robust condition number estimate is proven for the new reduced-dimension adaptive GDSW method which is also valid for existing adaptive GDSW methods. Numerical results for the equations of isotropic linear elasticity in three dimensions confirming the theoretical findings are presented.@en

Two-level overlapping Schwarz domain decomposition methods for second-order elliptic problems in two dimensions are proposed using coarse spaces constructed from the Approximate Component Mode Synthesis (ACMS) multiscale discretization approach. These coarse spaces are based on eigenvalue problems using Schur complements on subdomain edges. It is then shown that the convergence of the resulting preconditioned Krylov method can be controlled by a user-specified tolerance and thus can be made independent of heterogeneities in the coefficient of the partial differential equation. The relations of this new approach to other known adaptive coarse space approaches for overlapping Schwarz methods are also discussed. Compared to one of the competing adaptive approaches, the new coarse space can be significantly smaller. Compared to other competing approaches, the eigenvalue problems are significantly cheaper to solve, i.e., the dimension of the eigenvalue problems is minimal among the competing adaptive approaches under consideration. Our local eigenvalue problems can be solved using one iteration of LobPCG for essentially the same cost as a Cholesky-decomposition of a Schur complement on a subdomain edge.@en

A robust two-level overlapping Schwarz method for scalar elliptic model problems with highly varying coefficient functions is introduced. While the convergence of standard coarse spaces may depend strongly on the contrast of the coefficient function, the condition number bound of the new method is independent of the coefficient function. Indeed, the condition number only depends on a user-prescribed tolerance. The coarse space is based on discrete harmonic extensions of vertex, edge, and face interface functions, which are computed from the solutions of corresponding local generalized edge and face eigenvalue problems. The local eigenvalue problems are of the size of the edges and faces of the decomposition, and the eigenvalue problems can be constructed solely from the local subdomain stiffness matrices and the fully assembled global stiffness matrix. The new AGDSW (adaptive generalized Dryja-Smith-Widlund) coarse space always contains the classical GDSW coarse space by construction of the generalized eigenvalue problems. Numerical results supporting the theory are presented for several model problems in three dimensions using structured as well as unstructured meshes and unstructured decompositions.@en

A robust two-level overlapping Schwarz method for scalar elliptic model problems with highly varying coefficient functions is introduced. While the convergence of standard coarse spaces may depend strongly on the contrast of the coefficient function, the condition number bound of the new method is independent of the coefficient function. Indeed, the condition number only depends on a user-prescribed tolerance. The coarse space is based on discrete harmonic extensions of vertex, edge, and face interface functions, which are computed from the solutions of corresponding local generalized edge and face eigenvalue problems. The local eigenvalue problems are of the size of the edges and faces of the decomposition, and the eigenvalue problems can be constructed solely from the local subdomain stiffness matrices and the fully assembled global stiffness matrix. The new AGDSW (adaptive generalized Dryja-Smith-Widlund) coarse space always contains the classical GDSW coarse space by construction of the generalized eigenvalue problems. Numerical results supporting the theory are presented for several model problems in three dimensions using structured as well as unstructured meshes and unstructured decompositions.@en

We propose robust coarse spaces for two-level overlapping Schwarz preconditioners, which are extensions of the energy minimizing coarse space known as GDSW (Generalized Dryja, Smith, Widlund). The resulting two-level methods with adaptive coarse spaces are robust for second order elliptic problems in two dimensions, even in presence of a highly heterogeneous coefficient function, and reduce to the standard GDSW algorithm if no additional coarse basis functions are used.@en

MRI (Magnetic Resonance Imaging) measurements and CFD (Computational Fluid Dynamics) simulations for blood flow in intracranial aneurysms are compared for a benchmark problem. In particular, it is shown that noise and other artifacts in the MRI measurements have an influence on certain properties of the flow field, e.g., on the boundary flow and mass conservation.@en

MRI (Magnetic Resonance Imaging) measurements and CFD (Computational Fluid Dynamics) simulations for blood flow in intracranial aneurysms are compared for a benchmark problem. In particular, it is shown that noise and other artifacts in the MRI measurements have an influence on certain properties of the flow field, e.g., on the boundary flow and mass conservation.@en

A benchmark for the comparison of MRI (Magnetic Resonance Imaging) measurements and CFD (Computational Fluid Dynamics) simulations for blood flow in intracranial aneurysms is presented. The benchmark setting is designed to allow for CFD simulations that are completely independent of the MRI measurements. This facilitates a fair comparison of both methods. Furthermore, results showing the good agreement of MRI and CFD are presented.@en

A benchmark for the comparison of MRI (Magnetic Resonance Imaging) measurements and CFD (Computational Fluid Dynamics) simulations for blood flow in intracranial aneurysms is presented. The benchmark setting is designed to allow for CFD simulations that are completely independent of the MRI measurements. This facilitates a fair comparison of both methods. Furthermore, results showing the good agreement of MRI and CFD are presented.@en