
Parallel NewtonKrylovBDDC and FETIDP deluxe solvers for implicit time discretizations of the cardiac Bidomain equations
Two novel parallel NewtonKrylov Balancing Domain Decomposition by Const...
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Nonasymptotic Superlinear Convergence of Standard QuasiNewton Methods
In this paper, we study the nonasymptotic superlinear convergence rate ...
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On the Globalization of ASPIN Employing TrustRegion Control Strategies – Convergence Analysis and Numerical Examples
The parallel solution of large scale nonlinear programming problems, wh...
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Acceleration of nonlinear solvers for natural convection problems
This paper develops an efficient and robust solution technique for the s...
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Highaccuracy time discretization of stochastic fractional diffusion equation
A highaccuracy time discretization is discussed to numerically solve th...
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Rational spectral filters with optimal convergence rate
In recent years, contourbased eigensolvers have emerged as a standard a...
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An oscillationfree fully partitioned scheme for the numerical modeling of cardiac active mechanics
In silico models of cardiac electromechanics couple together mathematica...
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NewtonKrylovBDDC deluxe solvers for nonsymmetric fully implicit time discretizations of the Bidomain model
A novel theoretical convergence rate estimate for a Balancing Domain Decomposition by Constraints algorithm is proven for the solution of the cardiac Bidomain model, describing the propagation of the electric impulse in the cardiac tissue. The nonlinear system arises from a fully implicit time discretization and a monolithic solution approach. The preconditioned nonsymmetric operator is constructed from the linearized system arising within the NewtonKrylov approach for the solution of the nonlinear problem; we theoretically analyze and prove a convergence rate bound for the Generalised Minimal Residual iterations' residual. The theory is confirmed by extensive parallel numerical tests, widening the class of robust and efficient solvers for implicit time discretizations of the Bidomain model.
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