arXiv subjects

Fatemeh Chegini

Publications and source records attributed to Fatemeh Chegini.

4 recordsLinked to original sources

arXiv2025

Computing the Full Earth System at 1 km Resolution

We present the first-ever global simulation of the full Earth system at 1.25 km grid spacing, achieving highest time compression with an unseen number of degrees of freedom. Our model captures the flow of energy, water, and carbon through key components of the Earth system: atmosphere, ocean, and land. To achieve this landmark simulation, we harness the power of 8192 GPUs on Alps and 20480 GPUs on JUPITER, two of the world's largest GH200 superchip installations. We use both the Grace CPUs and Hopper GPUs by carefully balancing Earth's components in a heterogeneous setup and optimizing acceleration techniques available in ICON's codebase. We show how separation of concerns can reduce the code complexity by half while increasing performance and portability. Our achieved time compression of 145.7 simulated days per day enables long studies including full interactions in the Earth system and even outperforms earlier atmosphere-only simulations at a similar resolution.

physics.ao-ph↗

arXiv2025

A BDDC Preconditioner for the Cardiac EMI Model in three Dimensions

We analyze a Balancing Domain Decomposition by Constraints (BDDC) preconditioner for the solution of three dimensional composite Discontinuous Galerkin discretizations of reaction-diffusion systems of ordinary and partial differential equations arising in cardiac cell-by-cell models like the Extracellular space, Membrane and Intracellular space (EMI) Model. These microscopic models are essential for the understanding of events in aging and structurally diseased hearts which macroscopic models relying on homogenized descriptions of the cardiac tissue, like Monodomain and Bidomain models, fail to adequately represent. The modeling of each individual cardiac cell results in discontinuous global solutions across cell boundaries, requiring the careful construction of dual and primal spaces for the BDDC preconditioner. We provide a scalable condition number bound for the precondition operator and validate the theoretical results with extensive numerical experiments.

math.NA↗

arXiv2025

Convergence analysis of BDDC preconditioners for composite DG discretizations of the cardiac cell-by-cell model

A Balancing Domain Decomposition by Constraints (BDDC) preconditioner is constructed and analyzed for the solution of composite Discontinuous Galerkin discretizations of reaction-diffusion systems of ordinary and partial differential equations arising in cardiac cell-by-cell models. Unlike classical Bidomain and Monodomain cardiac models, which rely on homogenized descriptions of cardiac tissue at the macroscopic level, the cell-by-cell models enable the representation of individual cardiac cells, cell aggregates, damaged tissues, and nonuniform distributions of ion channels on the cell membrane. The resulting discrete cell-by-cell models exhibit discontinuous global solutions across the cell boundaries. Therefore, the proposed BDDC preconditioner employs appropriate dual and primal spaces with additional constraints to transfer information between cells (subdomains) without affecting the overall discontinuity of the global solution. A scalable convergence rate bound is proved for the resulting BDDC cell-by-cell preconditioned operator, while numerical tests validate this bound and investigate its dependence on the discretization parameters.

math.NA↗

arXiv2023

Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods

The locality of solution features in cardiac electrophysiology simulations calls for adaptive methods. Due to the overhead incurred by established mesh refinement and coarsening, however, such approaches failed in accelerating the computations. Here we investigate a different route to spatial adaptivity that is based on nested subset selection for algebraic degrees of freedom in spectral deferred correction methods. This combination of algebraic adaptivity and iterative solvers for higher order collocation time stepping realizes a multirate integration with minimal overhead. This leads to moderate but significant speedups in both monodomain and cell-by-cell models of cardiac excitation, as demonstrated at four numerical examples.

math.NA↗