Publications by Toni Mikael Lassila

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We consider Isogeometric Analysis in the framework of the Galerkin method for the spatial approximation of cardiac electrophysiology models defined on NURBS surfaces; specifically, we perform a numerical comparison between basis functions of degree p >= 1 ...

This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities – which are mainly related either to nonlin ...

We present a coupling of the reduced basis methods and free-form deformations for shape optimization and design of systems modelled by elliptic PDEs. The free-form deformations give a parameterization of the shape that is independent of the mesh, the initi ...

A reduced-order strategy based on the reduced basis (RB) method is developed for the efficient numerical solution of statistical inverse problems governed by PDEs in domains of varying shape. Usual discretization techniques are infeasible in this context, ...

Mathematical modeling of the human heart and its function can expand our understanding of various cardiac diseases, which remain the most common cause of death in the developed world. Like other physiological systems, the heart can be understood as a compl ...

The solution of inverse problems in cardiovascular mathematics is computationally expensive. In this paper we apply a domain parametrization technique to reduce both the geometrical and computational complexity of the forward problem, and replace the finit ...

We present a new model reduction technique for steady fluid-structure interaction problems. When the fluid domain deformation is suitably parametrized, the coupling conditions between the fluid and structure can be formulated in the low-dimensional space o ...

We present a model for the electrophysiology in the heart to handle the electrical propagation through the Purkinje system and in the myocardium, with two-way coupling at the Purkinje-muscle junctions. In both the subproblems the monodomain model is consid ...

A new approach for computationally efficient estimation of stability factors for parametric partial differential equations is presented. The general parametric bilinear form of the problem is approximated by two affinely parametrized bilinear forms at diff ...

We propose an improvement to the reduced basis method for parametric partial differential equations. An assumption of affine parameterization leads to an efficient offline-online decomposition when the problem is solved for many different parametric config ...

Reduced basis approximations for geometrically parametrized advection- diffusion equations are investigated. The parametric domains are assumed to be images of a reference domain through a piecewise polynomial map; this may lead to nonaffinely parametrized ...

Verification of the computation of local quantities of interest, e.g. the displacements at a point, the stresses in a local area and the stress intensity factors at crack tips, plays an important role in improving the structural design for safety. In this ...

The complex phenomena underlying mechanical contraction of cardiac cells and their influence in the dynamics of ventricular contraction are extremely important in understanding the overall function of the heart. In this paper we generalize previous contrib ...

Toni Mikael Lassila

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Isogeometric approximation of cardiac electrophysiology models on surfaces: An accuracy study with application to the human left atrium

Model order reduction in fluid dynamics: challenges and perspectives

Parametric free-form shape design with PDE models and reduced basis method

A reduced-order strategy for solving inverse Bayesian shape identication problems in physiological flows

Integrated Heart-Coupling multiscale and multiphysics models for the simulation of the cardiac function

A reduced computational and geometrical framework for inverse problems in haemodynamics

A reduced basis model with parametric coupling for fluid-structure interaction problems

A coupled 3D-1D numerical monodomain solver for cardiac electrical activation in the myocardium with detailed Purkinje network

On the approximation of stability factors for general parametrized partial differential equations with a two-level affine decomposition

Model reduction of semiaffinely parameterized partial differential equations by two-level affine approximation

Accurate solution of Bayesian inverse uncertainty quantification problems combining reduced basis methods and reduction error models

Reduced basis approximation for shape optimization in thermal flows with a parametrized polynomial geometric map

Computing upper and lower bounds for linear outputs of elasticity by the smoothed finite element method

Thermodynamically consistent orthotropic activation model capturing ventricular systolic wall thickening in cardiac electromechanics