A5085498434- Numerical methods for differential equations
- Advanced Numerical Methods in Computational Mathematics
- Matrix Theory and Algorithms
- Computational Fluid Dynamics and Aerodynamics
- Differential Equations and Numerical Methods
- Modeling and Simulation Systems
- Model Reduction and Neural Networks
- Cardiovascular Function and Risk Factors
- Advanced MRI Techniques and Applications
- Iterative Learning Control Systems
- Advanced Control Systems Optimization
- Cardiac Arrhythmias and Treatments
- Dynamics and Control of Mechanical Systems
- Nonlinear Dynamics and Pattern Formation
- Fractional Differential Equations Solutions
- Cardiac Imaging and Diagnostics
- Advanced Algebra and Logic
- Advanced Mathematical Modeling in Engineering
- Electromagnetic Simulation and Numerical Methods
- Spectroscopy and Quantum Chemical Studies
- Iterative Methods for Nonlinear Equations
- Differential Equations and Boundary Problems
- Numerical Methods and Algorithms
- Fluid Dynamics and Turbulent Flows
- Simulation Techniques and Applications
Lund University
2010-2023
Statistics Sweden
2011-2015
Numerical Method (China)
1990-2006
Faculty (United Kingdom)
2005
Simón Bolívar University
1995
University of Cambridge
1993
Swedish Institute
1989
KTH Royal Institute of Technology
1982-1989
Radboud University Nijmegen
1985
A new index reduction algorithm for DAEs is developed. In the usual manner, parts of DAE are differentiated analytically and appended to original system. For each additional equation, a derivative selected be replaced by algebraic variable called dummy derivative. The resulting augmented system at most 1, but no longer overdetermined. derivatives not subject discretization; their purpose annihilate part dynamics in DAE, leaving only what corresponds state-space form. No constraint...
Adaptive time-stepping based on linear digital control theory has several advantages: the algorithms can be analyzed in terms of stability and adaptivity, they designed to produce smoother stepsize sequences resulting significantly improved regularity computational stability. Here, we extend this approach by viewing closed-loop transfer map H φ : logφ ↦ log h as a filter, processing signal (the principal error function) frequency domain, order smooth sequence . The covers all previously...
Adaptive step size control is difficult to combine with geometric numerical integration. As classical based on "past" information only, time symmetry destroyed and it the qualitative properties of method. In this paper we develop completely explicit, reversible, symmetry-preserving, adaptive selection algorithms for integrators such as Störmer--Verlet A new density controller proposed analyzed using backward error analysis reversible perturbation theory. For integrable systems show that...
In the numerical solution of ODEs by implicit time-stepping methods, a system (nonlinear) equations has to be solved each step. It is common practice use fixed-point iterations or, in stiff case, some modified Newton iteration. The convergence rate such methods depends on stepsize. Similarly, stepsize change may force refactorization iteration matrix solver. This paper develops new strategies for handling iterative nonlinear ODE solvers. These include automatic switching between and...
Abstract Background Functional and morphological changes of the heart influence blood flow patterns. Therefore, patterns may carry diagnostic prognostic information. Three-dimensional, time-resolved, three-directional phase contrast cardiovascular magnetic resonance (4D PC-CMR) can image with unique detail, using new visualization methods lead to insights. The aim this study is present validate a novel method quantitative potential for from 4D PC-CMR, called Volume Tracking, investigate if...
A new theory is presented, in which a generalized kinematic similarity transformation used to diagonalize linear differential systems. No matrices of Jordan form are needed. The relation Lyapunov's classical stability explored, and asymptotic estimates fundamental solutions given. Finally, some possible numerical applications the presented suggested.
To present and validate a new method for 4D flow quantification of vortex-ring mixing during early, rapid filling the left ventricle (LV) as potential index diastolic dysfunction heart failure.4D measurements were validated using planar laser-induced fluorescence (PLIF) in phantom setup. Controls (n = 23) failure patients studied at 1.5T (26 subjects) or 3T (20 to determine vortex volume (VV) inflowing (VVinflow ). The mixed into was quantified VVmix-in VV-VVinflow . ratio defined MXR /VV....
The prediction of stage values in implicit Runge--Kutta methods is important both for overall efficiency as well the design suitable control strategies method. purpose this paper to construct good value predictors and verify their behavior practical computations. We show that stiffly accurate low order it necessary use several predictors. In other words, a continuous extension method will not yield best results. also investigate how gain additional Newton iterations used correct error. This...