We present two MATLAB toolboxes, provided as open-source code, that expand the capabilities of the Control System Toolbox to large-scale models.

Predictive high-fidelity finite element simulations of human cardiac mechanics commonly require a large number of structural degrees of freedom. Additionally, these models are often coupled with lumped-parameter models of hemodynamics. High computational demands, however, slow down model calibration and therefore limit the use of cardiac simulations in clinical practice. As cardiac models rely on several patient-specific parameters, just one solution corresponding to one specific parameter set does not at all meet clinical demands. Moreover, while solving the nonlinear problem, 90% of the computation time is spent solving linear systems of equations. We propose to reduce the structural dimension of a monolithically coupled structure-Windkessel system by projection onto a lower-dimensional subspace. We obtain a good approximation of the displacement field as well as of key scalar cardiac outputs even with very few reduced degrees of freedom, while achieving considerable speedups. For subspace generation, we use proper orthogonal decomposition of displacement snapshots. Following a brief comparison of subspace interpolation methods, we demonstrate how projection-based model order reduction can be easily integrated into a gradient-based optimization.We demonstrate the performance of our method in a real-world multivariate inverse analysis scenario. Using the presented projection-based model order reduction approach can significantly speed up model personalization and could be used for many-query tasks in a clinical setting.cardiac mechanics, inverse analysis, parametric model order reduction, proper orthogonal decomposition 1 | INTRODUCTION Cardiac solid mechanics simulations consist of solving large-deformation, materially nonlinear, elastodynamic coupled boundary-value problems. There exist different approaches to incorporate blood flow into the computational model. Three-dimensional fluid-structure interaction is resolved for example in References 1 and 2. As the exact fluid dynamics of blood within the heart are, however, usually not needed, the structural model is commonly coupled to | Model order reductionThe needed huge number of degrees of freedom (DOFs) and other challenges of solving nonlinear problems make the solution of cardiac models computationally expensive and limit the models' use in clinical practice. For example, using a single node with 24 cores, a simulation of one heartbeat, which takes about 1 s in reality, takes about 1 d to compute with our high-fidelity four chamber model. 9 The potential to reduce computation time motivates the use of reduced order models (ROMs). In this work, we solely consider model order reduction (MOR) of time-dependent parametric problems. In the following, different strategies in reduced order modeling are reviewed.An important category of cardiac ROMs is made up by simplified modeling. For these models, the same system of differential equations as for the full order model (FOM) is solved, but on a simplified analytical geometry. The displacements are commonly param...

Moments of a transfer function 4 Rational Interpolation by Krylov subspace methods : i-th moment around Bases for input and output Krylov-subspaces: Moments from full and reduced order model around certain shifts match!

This paper presents a novel derivation for modal derivatives based on the Volterra series representation of nonlinear structural systems. After reviewing the classical derivation, new modal derivatives are proposed based on the employment of the Volterra theory and the variational equation approach. It turns out that the gained new derivatives are almost identical to the conventional ones, except for the fact that a sum/subtraction of eigenfrequencies results in our definition. In addition to the novel derivation, some possible impacts and applications of the new derivatives are presented and discussed, pursuing the aim that the conceptual results are also useful for practical purposes. 2376 COMPDYN 2019 7 th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering M. Papadrakakis, M. Fragiadakis (eds.

Dynamic systems with time-varying parameters arise in numerous industrial applications, e.g. in structural dynamics or systems with moving loads. A spatial discretization of such systems often leads to high-dimensional linear parameter-varying models, which need to be reduced in order to enable a fast simulation. In the following we present time-varying parametric model order reduction (p(t)MOR) based on matrix interpolation and apply this novel framework to a system with moving load. Model Reduction:• p(t)MOR by Matrix Interpolation applied• Order of locally reduced systems:Further study:• Interpretation of the new matrix Projective pMOR: Choose appropriate projection matrices to approximate the state-vector by . Application for Systems with Moving Loads Projective p(t)MOR:Analogously, we aim to approximate the state-vector by Systems with Moving Loads:• position of the acting load varies with time