Welcome

• Michael Hanke (KTH)
• Philipp Schlatter (KTH Mechanics)

Room: K1

A patient specific finite element model for high performance computer simulation of blood flow in the left ventricle of the human heart

• Jeannette Spühler (KTH HPCViz)

Room: K1 Computer simulation is emerging as a tool for increased understanding of normal heart function and cardiac diseases, and also to serve as decision support in diagnostics and treatment. The multidisciplinary nature of this problem poses interesting challenges and brings together expertise from various disciplines such as medicine, biomechanics, applied mathematics and computer science. Today's research is focused on various subproblems and the coupling of them in more complete models. Our interest lies in modeling the blood flow in the left ventricle (LV) by a finite element method. The model geometry of the LV is based on ultrasound measurements of the position of the inner wall of the LV at different time points during the cardiac cycle. We build a three dimensional mesh of tetrahedrons at the initial time and use mesh smoothing algorithms to deform the mesh so that it fits the moving surface geometry. An adaptive ALE space-time finite element solver based on continuous piecewise linear elements in space and time together with streamline diffusion stabilization is used to simulate the blood flow by solving the incompressible Navier-Stokes equations. The software used is the HPC branch of the open source FEM library DOLFIN and the adaptive flow solver Unicorn. Both libraries have been parallelized using a hybrid MPI+OpenMP approach. In this talk we present recent work in enhancing the model by embedding the models of the aortic valves and expanding the problem statement to the realm of fluid-structure interaction.

A numerical investigation of the cell sorting based on the deformability

• Lailai Zhu (KTH Mechanics, Linne flow centre)

Room: K1 We develop a code to resolve the fluid-structure interaction of capsules in low-Reynolds-number flow, in 3D general geometries. We use accelerated boundary integral method general geometry Ewald method (GGEM), in the framework of the Navier-Stokes solver NEK5000 based on spectral element method. A global spectral interpretation employing spherical harmonics is incorporated simultaneously to resolve the membrane dynamics. Two cases are investigated to illustrate the generality of our implementation. We firstly show a capsule transported in a 3D channel and/or duct with a 90 degree straight and/or smooth curved corner, for a better understanding of moving soft objects in geometrically asymmetric configurations. We examine the effect of capsule elasticity and wall confinement in detail. Our results give useful hints for the design of micro-devices. As a second case, we simulate the capsule in flow past a cylindrical obstacle with and without confinement, representing two popular cell separation configurations, pinched flow fractionation (PFF) and deterministic lateral displacement (DLL) respectively. In contrast to the original methodology using fluid inertia, particle size or steric effect, we numerically demonstrate the pure-elasticity-driven cell separation in such devices.

Fast simulation of particle suspensions using double layer boundary integrals and spectral Ewald summation

• Ludvig af Klinteberg (KTH Numerical Analysis)

Room: K1 We present a method for simulating periodic suspensions of sedimenting rigid particles, based on a boundary integral solution of the Stokes flow equations. The purpose of our work is to improve the understanding of the large scale properties of suspensions by looking at the microscale interactions between individual particles. Boundary integral methods are attractive for this problem type due to high attainable accuracy, depending on the underlying quadrature method, and a reduction of the problem dimensionality from three to two. However, the resulting discrete systems have full matrices, and require the use of fast algorithms for efficient solution. Our method is based on a periodic version of the completed double layer boundary integral formulation for Stokes flow, which yields a well-conditioned system that converges rapidly when solved iteratively using GMRES. The discrete system is formulated using the Nyström method, and the singular integrals of the formulation are treated using singularity subtraction. The method is accelerated by a spectrally accurate fast Ewald summation method, which allows us to compute the single and double layer potentials of the formulation in O(N log N) time. By developing accurate estimates for the truncation errors of the Ewald summation, we are able to choose the parameters of the fast method such that the computation time is optimal for a given error tolerance.

Keynote: Bifurcation analysis for timesteppers

• Laurette Tuckerman

Room: K1 For systems making a transition from simple (uniform, laminar, steady) to more complex (non-uniform, periodic, quasiperiodic, chaotic, turbulent) behavior, a bifurcation diagram summarizes the information necessary for understanding the system. A complete bifurcation diagram, including unstable states and limit cycles, is inaccessible to experiment, but is, in principle, obtainable numerically from the governing equations. This is seldom done in practice if the equations are two or three dimensional PDEs. In this talk, we will show how to adapt a time-stepping code so as to calculate steady states and rotating waves via Newton's method and to calculate leading eigenpairs and Floquet multipliers via the Arnoldi method. We will show how this information can be used to understand various hydrodynamic pattern-forming systems, such as convection in cylindrical and spherical geometries.

Multiscale modeling in Neuroscience: numerical challenges in multiscale simulation framework development.

• Ekaterina Brocke (KTH CSC CB)

Room: K1 Multiscale modeling attracts an increasing number of neuroscientists to study how different levels of organization (networks of neurons, cells, synapses, biochemical level) interact with each other across multiple scales of space and time to mediate different brain functions. Different scales can be described by different physical and mathematical formalisms thus making it non trivial to connect the scales in terms of both mathematical and practical challenges. With the aim of getting a grasp of the task complexity, we developed several multiscale models constituted from small models simulated in different neural simulation environments and connected through Python. In this talk, we will discuss numerical challenges which arise from these initial steps as well as the requirements for building a simulation framework that will support multiscale co-simulations.

Keynote: Scientific Computing from a historical perspective

• Bertil Gustafsson

Room: K1 Mathematical models for physical processes took a giant leap when Isaac Newton formulated the basic laws of mechanics by using differential calculus. In the following centuries there was a rapid development of mathematical models for an ever increasing number of scientific and engineering processes. However, the models are in the form of differential equations, and in order to make any use of them for real applications, one has to find the solution in an explicit analytic form that can be evaluated at any different point in time and space. Except for very simple problems, this is impossible. This difficulty is overcome by the use of numerical methods based on some kind of approximation of the mathematical model. Such methods were developed for many problems centuries ago, but their impact were very limited due to the heavy computations that were required. The introduction of electronic computers changed the situation completely. Already known numerical methods could be implemented and the results could be used for practical and difficult problems. Furthermore, an almost explosive development of new numerical methods took place in parallel with the fast development of computers. In addition to theory and experiments, science got a third leg: scientific computing. In this talk we shall give a survey of the most important steps of this process, with emphasis on the development of numerical methods. Furthermore, we shall discuss the special influence of Swedish researchers, and how it happened that Sweden got a significant position on the world map of scientific computing.

Inclusion of many-body methods in density functional theory

• Andreas Östlin (KTH Royal Institute of Technology)

Room: K1 Density functional theory (DFT) has over the years proven to be highly successful in describing the electronic structure of real materials. Today, there exists several methods based on DFT that can calculate the electronic structure from first-principles, i.e. without any need for experimental input. However, DFT will often fail in the case of so called strongly correlated materials, where the interaction between electrons plays a leading role in determining the behaviour of the material. Examples of these kinds of materials can be found among the early transition metals and the rare-earths. During the recent decades dynamical mean field theory (DMFT) has shown great success in describing models of strongly correlated many-body systems. This has led to an increasing interest in the merging of DMFT with DFT in the hope of being able to describe strong correlations in real materials. We work on implementing DMFT in our own DFT method, the exact muffin-tin orbitals (EMTO) method. We will see some preliminary results of this work during this talk, and review the method with emphasis on numerical aspects.

Density Functional Theory studies of Graphene based Humidity Sensing

• Karim Elgammal (KTH - Department of Materials and Nano Physics)

Room: K1 Graphene has many interesting physical properties. Here, we are interested in investigating the possibility of using graphene as a humidity sensor. The graphene- water interaction has been evaluated using density functional theory (DFT). We have used the Quantum Esspresso as well as ELK (in elementary stage calculations) electronic structure codes. We report results where we have modeled single water molecules as well as a monolayer of water on the surface of graphene and evaluated the changes in the electronic structure of the graphene in the presence of water. We have utilized those high performance computing electronic structure enabled codes to be able to investigate such complicated systems in a speedy, accurate and efficient way taking advantage of optimized linear algebra libraries. This work is done in collaboration with experimentalists at KTH Royal Institute of Technology.

Conclusions

• Philipp Schlatter (KTH Mechanics)
• Michael Hanke (KTH)

Room: K1