SUMMARYWe propose two timestep selection algorithms, based on feedback control theory, for ÿnite element simulation of steady state and transient 2D viscous ow and coupled reaction-convection-di usion processes. To illustrate performance of the schemes in practice, we solve Rayleigh-Benard-Marangoni ows, ow across a backward-facing step, unsteady ow around a circular cylinder and chemical reaction systems. Numerical experiments conÿrm that the feedback controllers produce in some cases a very smooth stepsize variation, suggesting that robust control algorithms are possible. These experiments also show that parameter selection can improve timesteps when co-ordinated with the convergence control of non-linear iterations. Further, computational cost of the selection procedures is negligible, since they involve only storing a few extra vectors, computation of norms and evaluation of kinetic energy.

Immunotherapy has gained great momentum with chimeric antigen receptor T cell (CAR-T) therapy, in which patient’s T lymphocytes are genetically manipulated to recognize tumor-specific antigens, increasing tumor elimination efficiency. In recent years, CAR-T cell immunotherapy for hematological malignancies achieved a great response rate in patients and is a very promising therapy for several other malignancies. Each new CAR design requires a preclinical proof-of-concept experiment using immunodeficient mouse models. The absence of a functional immune system in these mice makes them simple and suitable for use as mathematical models. In this work, we develop a three-population mathematical model to describe tumor response to CAR-T cell immunotherapy in immunodeficient mouse models, encompassing interactions between a non-solid tumor and CAR-T cells (effector and long-term memory). We account for several phenomena, such as tumor-induced immunosuppression, memory pool formation, and conversion of memory into effector CAR-T cells in the presence of new tumor cells. Individual donor and tumor specificities are considered uncertainties in the model parameters. Our model is able to reproduce several CAR-T cell immunotherapy scenarios, with different CAR receptors and tumor targets reported in the literature. We found that therapy effectiveness mostly depends on specific parameters such as the differentiation of effector to memory CAR-T cells, CAR-T cytotoxic capacity, tumor growth rate, and tumor-induced immunosuppression. In summary, our model can contribute to reducing and optimizing the number of in vivo experiments with in silico tests to select specific scenarios that could be tested in experimental research. Such an in silico laboratory is an easy-to-run open-source simulator, built on a Shiny R-based platform called CARTmath. It contains the results of this manuscript as examples and documentation. The developed model together with the CARTmath platform have potential use in assessing different CAR-T cell immunotherapy protocols and its associated efficacy, becoming an accessory for in silico trials.

SUMMARY The effects of reordering the unknowns on the convergence of incomplete factorization preconditioned Krylov subspace methods are investigated. Of particular interest is the resulting preconditioned iterative solver behavior when adaptive mesh refinement and coarsening (AMR/C) are utilized for serial or distributed parallel simulations. As representative schemes, we consider the familiar reverse Cuthill–McKee and quotient minimum degree algorithms applied with incomplete factorization preconditioners to CG and GMRES solvers. In the parallel distributed case, reordering is applied to local subdomains for block ILU preconditioning, and subdomains are repartitioned dynamically as mesh adaptation proceeds. Numerical studies for representative applications are conducted using the object‐oriented AMR/C software system libMesh linked to the PETSc solver library. Serial tests demonstrate that global unknown reordering and incomplete factorization preconditioning can reduce the number of iterations and improve serial CPU time in AMR/C computations. Parallel experiments indicate that local reordering for subdomain block preconditioning associated with dynamic repartitioning because of AMR/C leads to an overall reduction in processing time. Copyright © 2011 John Wiley & Sons, Ltd.

SUMMARYThis work investigates the use of control strategies for timestep selection and convergence rate improvement of non-linear iterative processes in the ÿnite element solution of 2D coupled viscous ow and heat transfer. The present solution method employs a decoupled scheme, where the ÿnite element ow formulation is based on a penalty Galerkin method and the heat transfer computations use a traditional Galerkin formulation. We compare the e ciency of the control strategies for timestep selection with another heuristic adaptive stepsize selection scheme. Numerical results for representative Rayleigh-Benard-Marangoni problems conÿrm that the non-dimensional kinetic energy could be a suitable parameter to improve the timestep selection when co-ordinated with the convergence control of non-linear iterations. We ÿnd approximate solutions with a much smaller number of steps without any signiÿcant loss of accuracy.

SUMMARYThis work investigates partitioned iterative solution of coupled multiphysics systems including subcycling time-stepping strategies for decoupled subsystems in conjunction with a proportional-integral-derivative feedback control algorithm for adaptive time-step selection. Some basic algorithms are proposed and the total computational effort to integrate to steady state is compared for a representative coupled flow and heat transfer problem to illustrate the approach and assess performance efficiency.