Data Assimilation in Cardiovascular Fluid–Structure Interaction Problems: An Introduction
暂无分享,去创建一个
Alessandro Veneziani | Marta D'Elia | Mauro Perego | Luca Bertagna | A. Veneziani | M. Perego | M. D'Elia | L. Bertagna | Luca Bertagna
[1] Jeffrey K. Uhlmann,et al. Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.
[2] Max Gunzburger,et al. Perspectives in flow control and optimization , 1987 .
[3] R. E. Kalman,et al. A New Approach to Linear Filtering and Prediction Problems , 2002 .
[4] Assad A Oberai,et al. Elastic modulus imaging: some exact solutions of the compressible elastography inverse problem , 2007, Physics in medicine and biology.
[5] Rudolph van der Merwe,et al. The unscented Kalman filter for nonlinear estimation , 2000, Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No.00EX373).
[6] Thomas A. Manteuffel,et al. Weighted least-squares finite elements based on particle imaging velocimetry data , 2010, J. Comput. Phys..
[7] G. Rozza,et al. On the stability of the reduced basis method for Stokes equations in parametrized domains , 2007 .
[8] S. Salsa. Partial Differential Equations in Action: From Modelling to Theory , 2010 .
[9] Christian Vergara,et al. A Variational Approach for Estimating the Compliance of the Cardiovascular Tissue: An Inverse Fluid-Structure Interaction Problem , 2011, SIAM J. Sci. Comput..
[10] D. Zwillinger. Matrix Riccati Equations , 1992 .
[11] Stephen J. Wright,et al. Numerical Optimization , 2018, Fundamental Statistical Inference.
[12] K. Kunisch,et al. Numerical solutions for optimal control of monodomain equations , 2009 .
[13] Alfio Quarteroni,et al. Complex Systems in Biomedicine , 2006 .
[14] K. Kunisch,et al. Optimal control of the bidomain system (III): Existence of minimizers and first-order optimality conditions , 2013 .
[15] Gene H. Golub,et al. Matrix computations , 1983 .
[16] J. Halleux,et al. An arbitrary lagrangian-eulerian finite element method for transient dynamic fluid-structure interactions , 1982 .
[17] Karsten Urban,et al. A new error bound for reduced basis approximation of parabolic partial differential equations , 2012 .
[18] Christian Vergara,et al. Flow rate boundary problems for an incompressible fluid in deformable domains: Formulations and solution methods , 2010 .
[19] Assad A. Oberai,et al. Adjoint‐weighted variational formulation for the direct solution of inverse problems of general linear elasticity with full interior data , 2010 .
[20] Jeffrey Humpherys,et al. A Fresh Look at the Kalman Filter , 2012, SIAM Rev..
[21] F. Tröltzsch. Optimal Control of Partial Differential Equations: Theory, Methods and Applications , 2010 .
[22] Paul T. Boggs,et al. Sequential Quadratic Programming , 1995, Acta Numerica.
[23] Per Christian Hansen,et al. Rank-Deficient and Discrete Ill-Posed Problems , 1996 .
[24] J. Wolfowitz,et al. Introduction to the Theory of Statistics. , 1951 .
[25] K. Hinsch. Three-Dimensional Particle Velocimetry , 1995 .
[26] Kenichi Funamoto,et al. Reproduction of pressure field in ultrasonic‐measurement‐integrated simulation of blood flow , 2013, International journal for numerical methods in biomedical engineering.
[27] Karl Kunisch,et al. Estimation Techniques for Distributed Parameter Systems , 1989 .
[28] Y. Marzouk,et al. Large-Scale Inverse Problems and Quantification of Uncertainty , 1994 .
[29] Alfio Quarteroni,et al. Cardiovascular mathematics : modeling and simulation of the circulatory system , 2009 .
[30] M. Gunzburger,et al. Accuracy of least-squares methods for the Navier-Stokes equations , 1993 .
[31] K. Kunisch,et al. Optimal control of the bidomain system (II): uniqueness and regularity theorems for weak solutions , 2013 .
[32] Alessandro Veneziani,et al. Inverse Problems in Cardiovascular Mathematics , 2013 .
[33] H. Abou-Kandil,et al. Matrix Riccati Equations in Control and Systems Theory , 2003, IEEE Transactions on Automatic Control.
[34] P. Bochev. Analysis of Least-Squares Finite Element Methods for the Navier--Stokes Equations , 1997 .
[35] Marina Piccinelli,et al. Applications of variational data assimilation in computational hemodynamics , 2012 .
[36] Jan Modersitzki,et al. FAIR: Flexible Algorithms for Image Registration , 2009 .
[37] A. Veneziani,et al. Uncertainty quantification for data assimilation in a steady incompressible Navier-Stokes problem , 2013 .
[38] D. Chapelle,et al. Galerkin approximation with proper orthogonal decomposition : new error estimates and illustrative examples , 2012 .
[39] David Kilpatrick,et al. Estimation of the Bidomain Conductivity Parameters of Cardiac Tissue From Extracellular Potential Distributions Initiated by Point Stimulation , 2010, Annals of Biomedical Engineering.
[40] R. Glowinski,et al. Exact and approximate controllability for distributed parameter systems , 1995, Acta Numerica.
[41] E. Somersalo,et al. Statistical and computational inverse problems , 2004 .
[42] W. R. Taylor,et al. FLOW AND ATHEROSCLEROSIS , 2010 .
[43] Otmar Scherzer,et al. The use of Morozov's discrepancy principle for Tikhonov regularization for solving nonlinear ill-posed problems , 1993, Computing.
[44] Bert Fristedt,et al. Filtering and prediction , 2007 .
[45] Leiba Rodman,et al. Algebraic Riccati equations , 1995 .
[46] F. NOBILE,et al. An Effective Fluid-Structure Interaction Formulation for Vascular Dynamics by Generalized Robin Conditions , 2008, SIAM J. Sci. Comput..
[47] A. Patera,et al. Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations , 2007 .
[48] C. Vogel. Computational Methods for Inverse Problems , 1987 .
[49] H. Banks. A Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering , 2012 .
[50] Ionel M. Navon,et al. Data Assimilation for Geophysical Fluids , 2009 .
[51] Jeffrey K. Uhlmann,et al. New extension of the Kalman filter to nonlinear systems , 1997, Defense, Security, and Sensing.
[52] P. C. Franzone,et al. A PARALLEL SOLVER FOR REACTION-DIFFUSION SYSTEMS IN COMPUTATIONAL ELECTROCARDIOLOGY , 2004 .
[53] P. Moireau,et al. Sequential parameter estimation for fluid–structure problems: Application to hemodynamics , 2012, International journal for numerical methods in biomedical engineering.
[54] B. Fristedt,et al. Filtering and Prediction: A Primer , 2007 .
[55] Roland Glowinski,et al. Exact and Approximate Controllability for Distributed Parameter Systems: Index of subjects , 2008 .
[56] Giovanni Paolo Galdi,et al. Hemodynamical Flows: Modeling, Analysis and Simulation , 2008 .
[57] H. Engl,et al. Regularization of Inverse Problems , 1996 .
[58] Roland Glowinski,et al. Exact and Approximate Controllability for Distributed Parameter Systems: A Numerical Approach (Encyclopedia of Mathematics and its Applications) , 2008 .
[59] Alejandro F. Frangi,et al. Personalization of a cardiac electromechanical model using reduced order unscented Kalman filtering from regional volumes , 2013, Medical Image Anal..
[60] Pavel B. Bochev,et al. Least-Squares Finite Element Methods , 2009, Applied mathematical sciences.
[61] K. Hoffmann,et al. Optimal Control of Partial Differential Equations , 1991 .
[62] Damiano Lombardi,et al. Reduced-Order Modeling based on Approximated Lax Pairs , 2012 .
[63] Wing Kam Liu,et al. Lagrangian-Eulerian finite element formulation for incompressible viscous flows☆ , 1981 .
[64] Alessandro Veneziani,et al. Inverse problems in Cardiovascular Mathematics: toward patient‐specific data assimilation and optimization , 2013, International journal for numerical methods in biomedical engineering.
[65] Arye Nehorai,et al. Estimating Electrical Conductivity Tensors of Biological Tissues Using Microelectrode Arrays , 2012, 2012 Annual International Conference of the IEEE Engineering in Medicine and Biology Society.
[66] R. Dwight. Bayesian inference for data assimilation using least-squares finite element methods , 2010 .
[67] A. Quarteroni,et al. A reduced computational and geometrical framework for inverse problems in hemodynamics , 2013, International journal for numerical methods in biomedical engineering.
[68] Daniela Calvetti,et al. Introduction to Bayesian Scientific Computing: Ten Lectures on Subjective Computing , 2007 .
[69] Christian Vergara,et al. A New Approach to Numerical Solution of Defective Boundary Value Problems in Incompressible Fluid Dynamics , 2008, SIAM J. Numer. Anal..
[70] D. Chapelle,et al. Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems , 2011 .
[71] Kaare Brandt Petersen,et al. The Matrix Cookbook , 2006 .
[72] Alessandro Veneziani,et al. A Variational Data Assimilation Procedure for the Incompressible Navier-Stokes Equations in Hemodynamics , 2011, Journal of Scientific Computing.
[73] Jihui Zhang,et al. Infinitely many small solutions for the p(x)-Laplacian operator with nonlinear boundary conditions , 2013 .
[74] Bo Einarsson. Accuracy and Reliability in Scientific Computing , 2005, Software, Environments, Tools.