arXiv subjects

Clemens V. Verhoosel

Publications and source records attributed to Clemens V. Verhoosel.

16 recordsLinked to original sources

arXiv2026

Isogeometric Analysis for Explicit Wave Propagation in Poroelastic Media

For higher-order discretizations of explicit dynamics problems, Isogeometric Analysis (IGA) has several favorable properties as compared to classical Finite Element Analysis (FEA). While FEA produces spurious modes at orders beyond linear, this is not the case for IGA. Consequently, fewer degrees of freedom are required for comparable accuracy, larger timesteps can be taken, and the method is more robust for nonlinear problems. If outlier modes are removed, the timestep even becomes virtually independent of the order. In this paper, we investigate how these advantages apply to the poroelastic continuum model. We consider both a primal formulation, wherein our variables are the displacement of the matrix material, the fluid displacement, and the pressure, as well as a reduced form wherein the pressure is eliminated. For our discretizations, we employ divergence-conforming spline spaces. Conforming spline spaces for the fluid displacement ensure inf-sup stability for the primal form, as well as a correct null space in the reduced form. Furthermore, we prove and demonstrate that the two formulations coincide when both displacements are discretized with conforming spline spaces. Through spectral analysis, we find that the aforementioned benefits of IGA do carry over directly to the context of poroelasticity. In 1D, we split the discrete spectrum into fast and slow waves. When normalized against an analytical solution, each of these sub-spectra closely resembles results known in elasticity. Consequently, when poroelasticity is discretized with outlier-free IGA, the timestep is essentially independent of the order. We show this timestep scaling in 2D as well.

math.NA↗

arXiv2026

Data-driven moving-window Bayesian inference for transient CO2-temperature network models of buildings

In this work, we proposes a CO2-temperature network model that links multi-zone mass transport and thermal dynamics through shared latent drivers, airflow and occupancy. The thermal component is formulated as a resistance-capacitance (RC) network augmented with airflow-driven convective exchange, while the CO2 component is governed by inter-zonal convective transport. To calibrate the model and track time-varying operating conditions based on sparse sensing, we introduce a moving-window Bayesian inference procedure that jointly estimates thermal parameters, airflow and occupancy trajectories. The estimation also provides room-specific sensor noise levels, yielding posterior predictive forecasts with credible intervals. The framework is assessed using a controlled synthetic benchmark, and a scaled physical validation experiment using CO2 and temperature sensing. In both settings, the posterior accurately reconstructs trajectories within windows and delivers low forecast errors. When inference windows overlap abrupt regime transitions, the widened uncertainty bands and increased inferred noise levels provide an interpretable diagnostic of model-data mismatch, followed by rapid recovery once the new regime is observed. Overall, coupling CO2-informed airflow with thermal dynamics yields a robust approach for conductive and advective temperature prediction, supporting practical monitoring and energy-performance assessment under limited sensing.

math.NA↗

arXiv2026

Bayesian Model Selection for Complex Flows of Yield Stress Fluids

Modeling yield stress fluids in complex flow scenarios presents significant challenges, particularly because conventional rheological characterization methods often yield material parameters that are not fully representative of the intricate constitutive behavior observed in complex conditions. We propose a Bayesian uncertainty quantification framework for the calibration and selection of constitutive models for yield stress fluids, explicitly accounting for uncertainties in both modeling accuracy and experimental observations. The framework addresses the challenge of complex flow modeling by making discrepancies that emanate from rheological measurements explicit and quantifiable. We apply the Bayesian framework to rheological measurements and squeeze flow experiments on Carbopol 980. Our analysis demonstrates that Bayesian model selection yields robust probabilistic predictions and provides an objective assessment of model suitability through evaluated plausibilities. The framework naturally penalizes unnecessary complexity and shows that the optimal model choice depends on the incorporated physics, the prior information, and the availability of data. In rheological settings, the Herschel-Bulkley and biviscous power law models perform well. However, when these rheological outcomes are used as prior information for a rheo-informed squeeze flow analysis, a significant mismatch with the experimental data is observed. This is due to the yield stress inferred from rheological measurements not being representative of the complex squeeze flow case. In contrast, an expert-informed squeeze flow analysis, based on broader priors, yields accurate predictions. These findings highlight the limitations of translating rheological measurements to complex flows and underscore the value of Bayesian approaches in quantifying model bias and guiding model selection under uncertainty.

physics.flu-dyn↗

arXiv2024

A probabilistic reduced-order modeling framework for patient-specific cardio-mechanical analysis

Cardio-mechanical models can be used to support clinical decision-making. Unfortunately, the substantial computational effort involved in many cardiac models hinders their application in the clinic, despite the fact that they may provide valuable information. In this work, we present a probabilistic reduced-order modeling (ROM) framework to dramatically reduce the computational effort of such models while providing a credibility interval. In the online stage, a fast-to-evaluate generalized one-fiber model is considered. This generalized one-fiber model incorporates correction factors to emulate patient-specific attributes, such as local geometry variations. In the offline stage, Bayesian inference is used to calibrate these correction factors on training data generated using a full-order isogeometric cardiac model (FOM). A Gaussian process is used in the online stage to predict the correction factors for geometries that are not in the training data. The proposed framework is demonstrated using two examples. The first example considers idealized left-ventricle geometries, for which the behavior of the ROM framework can be studied in detail. In the second example, the ROM framework is applied to scan-based geometries, based on which the application of the ROM framework in the clinical setting is discussed. The results for the two examples convey that the ROM framework can provide accurate online predictions, provided that adequate FOM training data is available. The uncertainty bands provided by the ROM framework give insight into the trustworthiness of its results. Large uncertainty bands can be considered as an indicator for the further population of the training data set.

cs.CE↗

arXiv2024

Echocardiogram-based ventricular isogeometric cardiac analysis using multi-patch fitted NURBS

Monitoring the cardiac function often relies on non-invasive vital measurements, electrocardiograms, and low-resolution echocardiograms. The monitoring data can be augmented with numerical modeling results to support treatment-risk assessment. Often, medical images are not suitable for high-fidelity modeling due to their spatial sparsity and low resolution. In this work, we present a workflow that converts a limited number of two-dimensional (2D) echocardiogram images into analysis-suitable left-ventricle geometries using isogeometric analysis (IGA). The image data is fitted by reshaping a multi-patch NURBS template. This fitting procedure results in a smooth interpolation with a limited number of degrees of freedom. In addition, a coupled 3D-0D cardiac model is extended with a pre-stressing method to perform ventricular-cardiac-mechanic analyses based on in vivo images. The workflow is benchmarked using population-averaged imaging data, which demonstrates that both the shape of the left ventricle and its mechanical response are well predicted in sparse-data scenarios. The case of a clinical patient is considered to demonstrate the suitability of the workflow in a real-data setting.

physics.med-ph↗

arXiv2023

Uncertainty quantification for the squeeze flow of generalized Newtonian fluids

The calibration of rheological parameters in the modeling of complex flows of non-Newtonian fluids can be a daunting task. In this paper we demonstrate how the framework of Uncertainty Quantification (UQ) can be used to improve the predictive capabilities of rheological models in such flow scenarios. For this demonstration, we consider the squeeze flow of generalized Newtonian fluids. To systematically study uncertainties, we have developed a tailored squeeze flow setup, which we have used to perform experiments with glycerol and PVP solution. To mimic these experiments, we have developed a three-region truncated power law model, which can be evaluated semi-analytically. This fast-to-evaluate model enables us to consider uncertainty propagation and Bayesian inference using (Markov chain) Monte Carlo techniques. We demonstrate that with prior information obtained from dedicated experiments - most importantly rheological measurements - the truncated power law model can adequately predict the experimental results. We observe that when the squeeze flow experiments are incorporated in the analysis in the case of Bayesian inference, this leads to an update of the prior information on the rheological parameters, giving evidence of the need for recalibration in the considered complex flow scenario. In the process of Bayesian inference we also obtain information on quantities of interest that are not directly observable in the experimental data, such as the spatial distribution of the three flow regimes. In this way, besides improving the predictive capabilities of the model, the uncertainty quantification framework enhances the insight into complex flow scenarios.

physics.flu-dyn↗

arXiv2023

Stabilized immersed isogeometric analysis for the Navier-Stokes-Cahn-Hilliard equations, with applications to binary-fluid flow through porous media

Binary-fluid flows can be modeled using the Navier-Stokes-Cahn-Hilliard equations, which represent the boundary between the fluid constituents by a diffuse interface. The diffuse-interface model allows for complex geometries and topological changes of the binary-fluid interface. In this work, we propose an immersed isogeometric analysis framework to solve the Navier-Stokes-Cahn-Hilliard equations on domains with geometrically complex external binary-fluid boundaries. The use of optimal-regularity B-splines results in a computationally efficient higher-order method. The key features of the proposed framework are a generalized Navier-slip boundary condition for the tangential velocity components, Nitsche's method for the convective impermeability boundary condition, and skeleton- and ghost-penalties to guarantee stability. A binary-fluid Taylor-Couette flow is considered for benchmarking. Porous medium simulations demonstrate the ability of the immersed isogeometric analysis framework to model complex binary-fluid flow phenomena such as break-up and coalescence in complex geometries.

math.NA↗

arXiv2023

An isogeometric analysis framework for ventricular cardiac mechanics

The finite element method (FEM) is commonly used in computational cardiac simulations. For this method, a mesh is constructed to represent the geometry and, subsequently, to approximate the solution. To accurately capture curved geometrical features many elements may be required, possibly leading to unnecessarily large computation costs. Without loss of accuracy, a reduction in computation cost can be achieved by integrating geometry representation and solution approximation into a single framework using the Isogeometric Analysis (IGA) paradigm. In this study, we propose an IGA framework suitable for echocardiogram data of cardiac mechanics, where we show the advantageous properties of smooth splines through the development of a multi-patch anatomical model. A nonlinear cardiac model is discretized following the IGA paradigm, meaning that the spline geometry parametrization is directly used for the discretization of the physical fields. The IGA model is benchmarked with a state-of-the-art biomechanics model based on traditional FEM. For this benchmark, the hemodynamic response predicted by the high-fidelity FEM model is accurately captured by an IGA model with only 320 elements and 4,700 degrees of freedom. The study is concluded by a brief anatomy-variation analysis, which illustrates the geometric flexibility of the framework. The IGA framework can be used as a first step toward an efficient workflow for an improved understanding of, and clinical decision support for, the treatment of cardiac diseases like heart rhythm disorders.

physics.med-ph↗

arXiv2023

Critical time-step size analysis and mass scaling by ghost-penalty for immersogeometric explicit dynamics

In this article, we study the effect of small-cut elements on the critical time-step size in an immersogeometric context. We analyze different formulations for second-order (membrane) and fourth-order (shell-type) equations, and derive scaling relations between the critical time-step size and the cut-element size for various types of cuts. In particular, we focus on different approaches for the weak imposition of Dirichlet conditions: by penalty enforcement and with Nitsche's method. The stability requirement for Nitsche's method necessitates either a cut-size dependent penalty parameter, or an additional ghost-penalty stabilization term is necessary. Our findings show that both techniques suffer from cut-size dependent critical time-step sizes, but the addition of a ghost-penalty term to the mass matrix serves to mitigate this issue. We confirm that this form of `mass-scaling' does not adversely affect error and convergence characteristics for a transient membrane example, and has the potential to increase the critical time-step size by orders of magnitude. Finally, for a prototypical simulation of a Kirchhoff-Love shell, our stabilized Nitsche formulation reduces the solution error by well over an order of magnitude compared to a penalty formulation at equal time-step size.

math.NA↗

arXiv2022

Scan-based immersed isogeometric flow analysis

This chapter reviews the work conducted by our team on scan-based immersed isogeometric analysis for flow problems. To leverage the advantageous properties of isogeometric analysis on complex scan-based domains, various innovations have been made: (i) A spline-based segmentation strategy has been developed to extract a geometry suitable for immersed analysis directly from scan data; (ii) A stabilized equal-order velocity-pressure formulation for the Stokes problem has been proposed to attain stable results on immersed domains; (iii) An adaptive integration quadrature procedure has been developed to improve computational efficiency; (iv) A mesh refinement strategy has been developed to capture small features at a priori unknown locations, without drastically increasing the computational cost of the scan-based analysis workflow. We review the key ideas behind each of these innovations, and illustrate these using a selection of simulation results from our work. A patient-specific scan-based analysis case is reproduced to illustrate how these innovations enable the simulation of flow problems on complex scan data.

math.NA↗

arXiv2022

Residual-based error estimation and adaptivity for stabilized immersed isogeometric analysis using truncated hierarchical B-splines

We propose an adaptive mesh refinement strategy for immersed isogeometric analysis, with application to steady heat conduction and viscous flow problems. The proposed strategy is based on residual-based error estimation, which has been tailored to the immersed setting by the incorporation of appropriately scaled stabilization and boundary terms. Element-wise error indicators are elaborated for the Laplace and Stokes problems, and a THB-spline-based local mesh refinement strategy is proposed. The error estimation .and adaptivity procedure is applied to a series of benchmark problems, demonstrating the suitability of the technique for a range of smooth and non-smooth problems. The adaptivity strategy is also integrated in a scan-based analysis workflow, capable of generating reliable, error-controlled, results from scan data, without the need for extensive user interactions or interventions.

math.NA↗

arXiv2020

Unification of variational multiscale analysis and Nitsche's method, and a resulting boundary layer fine-scale model

We show that in the variational multiscale framework, the weak enforcement of essential boundary conditions via Nitsche's method corresponds directly to a particular choice of projection operator. The consistency, symmetry and penalty terms of Nitsche's method all originate from the fine-scale closure dictated by the corresponding scale decomposition. As a result of this formalism, we are able to determine the exact fine-scale contributions in Nitsche-type formulations. In the context of the advection-diffusion equation, we develop a residual-based model that incorporates the non-vanishing fine scales at the Dirichlet boundaries. This results in an additional boundary term with a new model parameter. We then propose a parameter estimation strategy for all parameters involved that is also consistent for higher-order basis functions. We illustrate with numerical experiments that our new augmented model mitigates the overly diffusive behavior that the classical residual-based fine-scale model exhibits in boundary layers at boundaries with weakly enforced essential conditions.

math.NA↗

arXiv2018

Robust and parallel scalable iterative solutions for large-scale finite cell analyses

The finite cell method is a highly flexible discretization technique for numerical analysis on domains with complex geometries. By using a non-boundary conforming computational domain that can be easily meshed, automatized computations on a wide range of geometrical models can be performed. Application of the finite cell method, and other immersed methods, to large real-life and industrial problems is often limited due to the conditioning problems associated with these methods. These conditioning problems have caused researchers to resort to direct solution methods, which signifi- cantly limit the maximum size of solvable systems. Iterative solvers are better suited for large-scale computations than their direct counterparts due to their lower memory requirements and suitability for parallel computing. These benefits can, however, only be exploited when systems are properly conditioned. In this contribution we present an Additive-Schwarz type preconditioner that enables efficient and parallel scalable iterative solutions of large-scale multi-level hp-refined finite cell analyses.

math.NA↗

arXiv2018

Skeleton-stabilized IsoGeometric Analysis: High-regularity Interior-Penalty methods for incompressible viscous flow problems

A Skeleton-stabilized IsoGeometric Analysis (SIGA) technique is proposed for incompressible viscous flow problems with moderate Reynolds number. The proposed method allows utilizing identical finite dimensional spaces (with arbitrary B-splines/NURBS order and regularity) for the approximation of the pressure and velocity components. The key idea is to stabilize the jumps of high-order derivatives of variables over the skeleton of the mesh. For B-splines/NURBS basis functions of degree $k$ with $C^α$-regularity ($0 \leq α< k$), only the derivative of order $α+1$ has to be controlled. This stabilization technique thus can be viewed as a high-regularity generalization of the (Continuous) Interior-Penalty Finite Element Method. Numerical experiments are performed for the Stokes and Navier-Stokes equations in two and three dimensions. Oscillation-free solutions and optimal convergence rates are obtained. In terms of the sparsity pattern of the algebraic system, we demonstrate that the block matrix associated with the stabilization term has a considerably smaller bandwidth when using B-splines than when using Lagrange basis functions, even in the case of $C^0$-continuity. This important property makes the proposed isogeometric framework practical from a computational effort point of view.

math.NA↗

arXiv2018

Skeleton-stabilized ImmersoGeometric Analysis for incompressible viscous flow problems

A Skeleton-stabilized ImmersoGeometric Analysis technique is proposed for incompressible viscous flow problems with moderate Reynolds number. The proposed formulation fits within the framework of the finite cell method, where essential boundary conditions are imposed weakly using a Nitsche-type method. The key idea of the proposed formulation is to stabilize the jumps of high-order derivatives of variables over the skeleton of the background mesh. The formulation allows the use of identical finite-dimensional spaces for the approximation of the pressure and velocity fields in immersed domains. The stability issues observed for inf-sup stable discretizations of immersed incompressible flow problems are avoided with this formulation. For B-spline basis functions of degree $k$ with highest regularity, only the derivative of order $k$ has to be controlled, which requires specification of only a single stabilization parameter for the pressure field. The Stokes and Navier-Stokes equations are studied numerically in two and three dimensions using various immersed test cases. Oscillation-free solutions and high-order optimal convergence rates can be obtained. The formulation is shown to be stable even in limit cases where almost every elements of the physical domain is cut, and hence it does not require the existence of interior cells. In terms of the sparsity pattern, the algebraic system has a considerably smaller stencil than counterpart approaches based on Lagrange basis functions. This important property makes the proposed skeleton-stabilized technique computationally practical. To demonstrate the stability and robustness of the method, we perform a simulation of fluid flow through a porous medium, of which the geometry is directly extracted from 3D $μ{CT}$ scan data.

math.NA↗

arXiv2016

A Multiscale Diffuse-Interface Model for Two-Phase Flow in Porous Media

In this paper we consider a multiscale phase-field model for capillarity-driven flows in porous media. The presented model constitutes a reduction of the conventional Navier-Stokes-Cahn-Hilliard phase-field model, valid in situations where interest is restricted to dynamical and equilibrium behavior in an aggregated sense, rather than a precise description of microscale flow phenomena. The model is based on averaging of the equation of motion, thereby yielding a significant reduction in the complexity of the underlying Navier-Stokes-Cahn-Hilliard equations, while retaining its macroscopic dynamical and equilibrium properties. Numerical results are presented for the representative 2-dimensional capillary-rise problem pertaining to two closely spaced vertical plates with both identical and disparate wetting properties. Comparison with analytical solutions for these test cases corroborates the accuracy of the presented multiscale model. In addition, we present results for a capillary-rise problem with a non-trivial geometry corresponding to a porous medium.

physics.flu-dyn↗