1,721,039 research outputs found
A comparison of Algebraic Multigrid Bidomain solvers on hybrid CPU–GPU architectures
Full text linkThe numerical simulation of cardiac electrophysiology is a highly challenging problem in scientific computing. The Bidomain system is the most complete mathematical model of cardiac bioelectrical activity. It consists of an elliptic and a parabolic partial differential equation (PDE), of reaction–diffusion type, describing the spread of electrical excitation in the cardiac tissue. The two PDEs are coupled with a stiff system of ordinary differential equations (ODEs), representing ionic currents through the cardiac membrane. Developing efficient and scalable preconditioners for the linear systems arising from the discretization of such computationally challenging model is crucial in order to reduce the computational costs required by the numerical simulations of cardiac electrophysiology. In this work, focusing on the Bidomain system as a model problem, we have benchmarked two popular implementations of the Algebraic Multigrid (AMG) preconditioner embedded in the PETSc library and we have studied the performance on the calibration of specific parameters. We have conducted our analysis on modern HPC architectures, performing scalability tests on multi-core and multi-GPUs settings. The results have shown that, for our problem, although scalability is verified on CPUs, GPUs are the optimal choice, since they yield the best performance in terms of solution time
Modeling ventricular repolarization: effects of transmural and apex-to-base heterogeneities in action potential durations
No full textAdvanced multiscale models in computational electrocardiology offer
a detailed representation of the heart bioelectrical activity,
ranging from the microscopic description of ion channels of the
cellular membrane to the macroscopic properties of anisotropic
front propagation in the whole heart. Our model consists of a
Monodomain or Bidomain tissue representation that includes
orthotropic anisotropy, transmural fiber rotation and
homogeneous or heterogeneous intrinsic membrane properties,
described by Luo-Rudy type models. We consider membrane heterogeneities
due either to the presence of midwall cells (M-cells) with different
action potential durations (APDs) or to the presence of subendocardial
ischemic regions. We present the results of large-scale simulations of
an entire heartbeat with epicardial or endocardial pacing of three-dimensional
ventricular blocks. We will also discuss some numerical features of our simulations,
including parallel scalability, multilevel preconditioning and space-time adaptivity
Monophasic action potentials generated by Bidomain modeling as a tool for detecting cardiac repolarization times
No full textWe analyse theoretical and by numerical simulations the relationship between
a unipolar electrogram at an exploring site , the unipolar
electrogram recorded at a permanentely depolarized site and a
reference potential . For equal anisotropic ratio between the intra and extracellular media,
when choosing the depolarized site as reference potential,
the electrogram at the exploring site usually called unipolar
monophasic action potential apart from scaling,
coincides with transmembrane action potential at the exploring site.
For general anisotropy others potential components must be added to
the previous transmembrane action potential component and we compare
the ideal monophasic action potential with the those
simulated for general anisotropy
Performance evaluation of cardiac repolarization markers derived from monophasic action potentials and unipolar electrograms: a simulation study
No full textPerformance evaluation of cardiac repolarization markers
derived from monophasic action potentials and unipolar electrograms using 3-dimensional parallel simulations of the bidomain models of the cardiac biolectric actitvitie
Overlapping Additive Schwarz preconditioners for isogeometric collocation discretizations of linear elasticity
Full text linkOverlapping Additive Schwarz (OAS) preconditioners are here constructed for isogeometric collocation discretizations of the system of linear elasticity in both two and three space dimensions. Isogeometric collocation methods are recent variants of isogeometric analysis based on the numerical approximation of the strong form of partial differential equations at appropriate collocation points. Numerical results in two and three dimensions show that two-level OAS preconditioners are scalable in the number of subdomains N, quasi-optimal with respect to the mesh size h and optimal with respect to the spline polynomial degree p. Moreover, two-level OAS preconditioners are more robust than one-level OAS and non-preconditioned GMRES solvers when the material tends to the incompressible limit, as well as in the presence of strong deformation of the NURBS geometry
Computational modeling of the electromechanical response of a ventricular fiber affected by eccentric hypertrophy
No full textThe aim of this work is to study the effects of eccentric hypertrophy on the electromechanics of a single myocardial ventricular fiber by means of a one-dimensional finite-element strongly-coupled model. The electrical current flow model is written in the reference configuration and it is characterized by two geometric feedbacks, i.e. the conduction and convection ones, and by the mechanoelectric feedback due to stretch-activated channels. First, the influence of such feedbacks is investigated for both a healthy and a hypertrophic fiber in case of isometric simulations. No relevant discrepancies are found when disregarding one or more feedbacks for both fibers. Then, all feedbacks are taken into account while studying the electromechanical responses of fibers. The results from isometric tests do not point out any notable difference between the healthy and hypertrophic fibers as regards the action potential duration and conduction velocity. The length-tension relationships show increased stretches and reduced peak values for tension instead. The tension-velocity relationships derived from afterloaded isotonic and quick-release tests depict higher values of contraction velocity at smaller afterloads. Moreover, higher maximum shortenings are achieved during the isotonic contraction. In conclusion, our simulation results are innovative in predicting the electromechanical behavior of eccentric hypertrophic fibers
Isogeometric block FETI-DP preconditioners for the Stokes and mixed linear elasticity systems
Full text linkThe aim of this work is to construct and analyze a FETI-DP type domain decomposition preconditioner for isogeometric discretizations of the Stokes and mixed linear elasticity systems. This method extends to the isogeometric analysis context the preconditioner previously proposed by Tu and Li (2015) for finite element discretizations of the Stokes system. The resulting isogeometric FETI-DP algorithm is proven to be scalable in the number of subdomains and has a quasi-optimal convergence rate bound which is polylogarithmic in the ratio of subdomain and element sizes. Extensive two-dimensional numerical experiments validate the theory, investigate the behavior of the preconditioner with respect to both the spline polynomial degree and regularity, and show its robustness with respect to domain deformation, material incompressibility and presence of elastic coefficient discontinuities across subdomain interfaces
On the virtual element method for topology optimization on polygonal meshes: A numerical study
Full text linkIt is well known that the solution of topology optimization problems may be affected both by the geometric properties of the computational mesh, which can steer the minimization
process towards local (and non-physical) minima, and by the accuracy of the method employed to discretize the underlying differential problem, which may not be able to
correctly capture the physics of the problem. In light of the above remarks, in this paper we consider polygonal meshes and employ the virtual element method (VEM) to solve
two classes of paradigmatic topology optimization problems, one governed by nearlyincompressible and compressible linear elasticity and the other by Stokes equations.
Several numerical results show the virtues of our polygonal VEM based approach with respect to more standard methods
A numerical investigation on the use of the virtual element method for topology optimization on polygonal meshes
Full text linkA classical formulation of topology optimization addresses the problem of finding the best distribution of an assigned amount of isotropic material that minimizes the work of the external forces at equilibrium. In general, the discretization of the volume-constrained minimum compliance problem resorts to the adoption of four node displacement-based finite elements, coupled with element-wise density unknowns.
When regular meshes made of square elements are used, well-known numerical instabilities arise, see in particular the so-called checkerboarded patterns. On the other hand, when unstructured meshes are needed to cope with geometry of any shape, additional instabilities can steer the optimizer towards local minima instead of the expected global one. Unstructured meshes approximate the strain energy of the members of the arising optimal design with an accuracy that is strictly related to the geometrical features of the discretization, thus remarkably affecting the achieved layouts.
In light of the above remarks, in this contribution we consider polygonal meshes and implement the virtual element method (VEM) to solve two classes of topology optimization problems. The robustness of the adopted discretization is exploited to address problems governed by (nearly incompressible and compressible) linear elasticity and problems governed by Stokes equations. Numerical results show the capabilities of the proposed polygonal VEM-based approach with respect to more conventional discretizations
- …
