Multiphysics Computational Modeling in $\boldsymbol{\mathcal{C}}\mathbf{Heart}$

Abstract

From basic science to translation, modern biomedical research demands computational models which integrate several interacting physical systems. This paper describes the infrastructural framework for generic multiphysics integration implemented in the software CHeart, a finite-element code for biomedical research. To generalize the coupling of physics systems, we introduce a framework in which the geometric and operator relationships between the constituent systems are rigorously defined. We then introduce the notion of topological interfaces and define specific operators encompassing many common model coupling requirements. These interfaces enable the evaluation of weak form integrals between mesh subregions of arbitrary finite-element bases' orders, types, and spatial dimensions. Equation maps are introduced which provide abstract representations of the individual physics systems that can be automatically combined to permit a monolithic matrix assembly. Flexible solution strategies for the resulting coupled systems are implemented, permitting fine-tuning of solution updates during fixed point iterations, and subgrouping where several problems are being solved together. Partitioning of coupled mesh domains for optimal load balancing is also supported, taking into account the per-processor cost of the entire coupled problem within the graph problem. The demonstration of the performance is illustrated through important real-world multiphysics problems relevant to cardiac physiology.

Convergence of the multigrid reduction in time algorithm for the linear elasticity equations

“…Scheme I is considered as the default scheme in our application code CHeart and is motivated by better conserving the energy in the system for large time step sizes (see Section 3.2; for more details, see other works). On the other hand, Scheme II is proposed as an improvement for parallel‐in‐time methods with the capability of predicting amplitudes of oscillation with comparable quality for practical time step sizes.…”

“…For the numerical experiments, the finite‐element software tool CHeart was employed. In CHeart, Scheme I was available as the default scheme for linear elasticity, whereas Scheme II was implemented as part of this work.…”

A transmurally heterogeneous orthotropic activation model for ventricular contraction and its numerical validation

“…Computational models can significantly help to increase the understanding of the heart function and dysfunction. As the computing power increases, electromechanical and electro‐fluid‐mechanical models of the heart have been developed and numerically solved . Unfortunately, the real predictive capabilities of such models are not always clear.…”

“…As the computing power increases, electromechanical and electro-fluid-mechanical models of the heart have been developed and numerically solved. 1,[3][4][5][6][7][8][9][10] Unfortunately, the real predictive capabilities of such models are not always clear. In fact, many models fail in capturing the most obvious characteristics of the heart deformation.…”

Validation of a non‐conforming monolithic fluid‐structure interaction method using phase‐contrast MRI

“…CHeart —a multi‐physics software tool based on and the matrix solver MUMPS were used to solve the considered problem on compute nodes with 2 x Intel(R) Xeon® CPU E5‐2680 v2 (2.80 GHz) with 10 cores, 256 GB RAM and 4 × 500 GB Samsung SSD (network with 1 x QDR‐Infiniband Interconnect (40 GBit) and 1 × 1 GBit Ethernet).…”