| Abstract: | In studying biomechanical deformation in articular cartilage, the presence ofcells (chondrocytes) necessitates the consideration of inhomogeneous elasticityproblems in which cells are idealized as soft inclusions within a stiff extracellular matrix.An analytical solution of a soft inclusion problem is derived and used toevaluate iterative numerical solutions of the associated linear algebraicsystem based on discretization via the finite element method, and use of aniterative conjugate gradient method with algebraic multigrid preconditioning (AMG-PCG).Accuracy and efficiency of the AMG-PCG algorithm is compared to two otherconjugate gradient algorithms with diagonal preconditioning (DS-PCG) or amodified incomplete LU decomposition (Euclid-PCG) based on comparison to the analytical solution.While all three algorithms are shown to be accurate, the AMG-PCG algorithmis demonstrated to provide significant savings in CPU time as the number of nodal unknowns is increased.In contrast to the other two algorithms, the AMG-PCG algorithm alsoexhibits little sensitivity of CPU time and number of iterations tovariations in material properties that are known to significantly affect model variables.Results demonstrate the benefits of algebraic multigrid preconditionersfor the iterative solution of assembled linear systems based on finiteelement modeling of soft elastic inclusion problems and may be particularlyadvantageous for large scale problems with many nodal unknowns. |
