# Matthias MöllerDelft University of Technology | TU · Department of Applied Mathematics

Matthias Möller

Dr. rer.nat.

## About

112

Publications

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1,284

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Introduction

Additional affiliations

September 2013 - April 2021

November 2012 - August 2013

August 2009 - October 2012

## Publications

Publications (112)

Wrinkling is the phenomenon of out-of-plane deformation patterns in thin walled structures, as a result of a local compressive (internal) loads in combination with a large membrane stiffness and a small but non-zero bending stiffness. Numerical modelling typically involves thin shell formulations. As the mesh resolution depends on the wrinkle wave...

Isogeometric analysis has brought a paradigm shift in integrating computational simulations with geometric designs across engineering disciplines. This technique necessitates analysis-suitable parameterization of physical domains to fully harness the synergy between Computer-Aided Design and Computer-Aided Engineering analyses. Existing methods oft...

Mesh adaptivity is a technique to provide detail in numerical solutions without the need to refine the mesh over the whole domain. Mesh adaptivity in isogeometric analysis can be driven by Truncated Hierarchical B-splines (THB-splines) which add degrees of freedom locally based on finer B-spline bases. Labeling of elements for refinement is typical...

We propose a method for optimizing the geometry of a freeform lens to redirect the light emitted from an extended source into a desired irradiance distribution. We utilize a gradient-based optimization approach with MITSUBA 3, an algorithmic differentiable non-sequential ray tracer that allows us to obtain the gradients of the freeform surface para...

In recent years, quantum Boltzmann methods have gained more and more interest as they might provide a viable path toward solving fluid dynamics problems on quantum computers once this emerging compute technology has matured and fault-tolerant many-qubit systems become available. The major challenge in developing a start-to-end quantum algorithm for...

Constructing high-quality structured meshes is a crucial preprocessing step in the simulation-based analysis of positive displacement machines and, in particular, rotary twin-screw compressors. Instead of creating these meshes directly, we resort to the computational paradigm of IsoGeometric Analysis (IGA) that integrates geometric modeling and num...

Numerical simulations of physical systems have become an indispensable third pillar in modern computational sciences and engineering (CSE) complementing theoretical and experimental analysis. Most numerical methods in use today like the finite element method (FEM), the boundary element method (BEM), the finite volume method (FVM), and the finite di...

Algorithmic differentiable ray tracing is a new paradigm that allows one to solve the forward problem of how light propagates through an optical system while obtaining gradients of the simulation results with respect to parameters specifying the optical system. Specifically, the use of algorithmically differentiable non-sequential ray tracing provi...

We propose a method for optimizing the geometry of a freeform lens to redirect the light emitted from an extended source into a desired irradiance distribution. We utilize a gradient-based optimization approach with MITSUBA 3, an algorithmic differentiable non-sequential ray tracer that allows us to obtain the gradients of the freeform surface para...

We propose a method for optimizing the geometry of a freeform lens to redirect the light emitted from an extended source into a desired irradiance distribution. We utilize a gradient-based optimization approach with MITSUBA 3, an algorithmic differentiable non-sequential ray tracer that allows us to obtain the gradients of the freeform surface para...

Various computational fluid dynamic simulations in engineering, such as external aerodynamics, only need the silhouette of an input geometry. Often, it is a laborious process that can take up many human hours. In addition, the CAD geometries are too complex and contain intricate features and topological holes. We showcase an effortless way to shrin...

Mesh adaptivity is a technique to provide detail in numerical solutions without the need to refine the mesh over the whole domain. Mesh adaptivity in isogeometric analysis can be driven by Truncated Hierarchical B-splines (THB-splines) which add degrees of freedom locally based on finer B-spline bases. Labeling of elements for refinement is typical...

Quantum computing began in 1980 with Paul A. Benioff’s theoretical feasibility study. Since then, it has brought a wealth of publications on quantum information theory, quantum technologies, algorithms, and potential applications. In this paper, we give a brief overview of developments in this field, focusing on their potential impact on scientific...

Parallel computing is omnipresent in today's scientific computer landscape, starting at multicore processors in desktop computers up to massively parallel clusters. While domain decomposition methods have a long tradition in computational mechanics to decompose spatial problems into multiple subproblems that can be solved in parallel, advancing sol...

Topology optimization is an increasingly popular tool for engineers to obtain lightweight yet stiff designs in an automated way. However, the design resolution is directly linked to the computational time required for the optimization. This is especially true for large-scale applications where a small design resolution is required. For instance, op...

Algorithmic differentiable ray tracing is a new paradigm that allows one to solve the forward problem of how light propagates through an optical system while obtaining gradients of the simulation results with respect to parameters specifying the optical system. Specifically, the use of algorithmically differentiable non-sequential ray tracing provi...

In recent years, quantum Boltzmann methods have gained more and more interest as they might provide a viable path towards solving fluid dynamics problems on quantum computers once this emerging compute technology has matured and fault-tolerant many-qubit systems become available. The major challenge in developing a start-to-end quantum algorithm fo...

We present a scalable algorithm for solving the collisionless Boltzmann equation in two and three spatial dimensions for variable grid sizes and discrete velocities on a fault-tolerant universal quantum computer. As a proof of concept of our collisionless quantum Boltzmann method (CQBM), we describe a full-circuit start-to-end implementation in Qis...

Much of recent progress in geophysics can be attributed to the adaptation of heterogeneous high-performance computing architectures. It is projected that the next major leap in many areas of science, and hence hopefully in geophysics too, will be due to the emergence of quantum computers. Finding a right combination of hardware, algorithms and a us...

Accelerating topology optimization using efficient algorithms on GPU hardware.

Structural mechanics is commonly modeled by (systems of) partial differential equations (PDEs). Except for very simple cases where analytical solutions exist, the use of numerical methods is required to find approximate solutions. However, for many problems of practical interest, the computational cost of classical numerical solvers running on clas...

Near term quantum devices have the potential to outperform classical computing through the use of hybrid classical-quantum algorithms such as Variational Quantum Eigensolvers. These iterative algorithms use a classical optimiser to update a parameterised quantum circuit. Each iteration, the circuit is executed on a physical quantum processor or qua...

The use of sequential time integration schemes becomes more and more the bottleneck within large-scale computations due to a stagnation of processor’s clock speeds. In this study, we combine the parallel-in-time Multigrid Reduction in Time method with a p -multigrid method to obtain a scalable solver specifically designed for Isogeometric Analysis....

This paper presents the benchmark score definitions of QPack, an application-oriented cross-platform benchmarking suite for quantum computers and simulators, which makes use of scalable Quantum Approximate Optimization Algorithm and Variational Quantum Eigensolver applications. Using a varied set of benchmark applications, an insight of how well a...

Triangulated meshes discretized from commercial CAD applications often possess a considerable level of complexity. However, when conducting external aerodynamics simulations at an earlier design stage, these meshes are way too complex and contain complex features and topological holes. We propose a practical and fast algorithm to shrink wrap triang...

Using the standard finite element method (FEM) to solve general partial differential equations, the round-off error is found to be proportional to $N^{\beta_{\rm R}}$, with $N$ the number of degrees of freedom (DoFs) and $\beta_{\rm R}$ a coefficient. A method which uses a few cheap numerical experiments is proposed to determine the coefficient of...

In this paper we present an approach to find quantum circuits suitable to mimic probabilistic and search operations on a physical NISQ device. We present both a gradient based and a non-gradient based machine learning approach to optimize the created quantum circuits. In our optimization procedure we make use of a cost function that differentiates...

Since its introduction in [20], Isogeometric Analysis (IgA) has established itself as a viable alternative to the Finite Element Method (FEM). Solving the resulting linear systems of equations efficiently remains, however, challenging when high-order B-spline basis functions of order \(p>1\) are adopted for approximation. The use of Incomplete LU (...

The paper gives an overview of Material Point Method and shows its evolution over the last 25 years. The Material Point Method developments followed a logical order. The article aims at identifying this order and show not only the current state of the art, but explain the drivers behind the developments and identify what is currently still missing....

Isogeometric Analysis (IgA) has become a viable alternative to the Finite Element Method (FEM) and is typically combined with a time integration scheme within the method of lines for time-dependent problems. However, due to a stagnation of processors clock speeds, traditional (i.e. sequential) time integration schemes become more and more the bottl...

Isogeometric Analysis [1] has become increasingly popular as an alternative to the Finite Element Method. Solving the resulting linear systems when adopting higher order B-spline basis functions remains a challenging task, as most (standard) iterative methods have a deteriorating preformance for higher values of the approximation order p.Recently,...

Modelling nonlinear phenomena in thin rubber shells calls for stretch-based material models, such as the Ogden model which conveniently utilizes eigenvalues of the deformation tensor. Derivation and implementation of such models have been already made in Finite Element Methods. This is, however, still lacking in shell formulations based on Isogeome...

This paper proposes a shape optimization algorithm based on the principles of Isogeometric Analysis (IGA) in which the parameterization of the geometry enters the problem formulation as an additional PDE-constraint. Inspired by the isoparametric principle of IGA, the parameterization and the governing state equation are treated using the same numer...

In finite element methods, the accuracy of the solution cannot increase indefinitely since the round-off error related to limited computer precision increases when the number of degrees of freedom (DoFs) is large enough. Because a priori information of the highest attainable accuracy is of great interest, we construct an innovative method to obtain...

In this paper, we present QPack, a benchmark for NISQ era quantum computers using QAOA algorithms. Unlike other evaluation metrics in the field, this benchmark evaluates not only one, but multiple important aspects of quantum computing hardware: the maximum problem size a quantum computer can solve, the required run-time, as well as the achieved ac...

Finding fast yet accurate numerical solutions to the Helmholtz equation remains a challenging task. The pollution error (i.e. the discrepancy between the numerical and analytical wave number k) requires the mesh resolution to be kept fine enough to obtain accurate solutions. A recent study showed that the use of Isogeometric Analysis (IgA) for the...

The first step towards applying isogeometric analysis techniques to solve PDE problems on a given domain consists in generating an analysis-suitable mapping operator between parametric and physical domains with one or several patches from no more than a description of the boundary contours of the physical domain. A subclass of the multitude of the...

Isogeometric Analysis can be considered as the natural extension of the Finite Element Method (FEM) to higher-order spline based discretizations simplifying the treatment of complex geometries with curved boundaries. Finding a solution of the resulting linear systems of equations efficiently remains, however, a challenging task. Recently, p-multigr...

This proceedings volume gathers a selection of outstanding research papers presented at the third Conference on Isogeometric Analysis and Applications, held in Delft, The Netherlands, in April 2018. This conference series, previously held in Linz, Austria, in 2012 and Annweiler am Trifels, Germany, in 2014, has created an international forum for in...

Over the years, Isogeometric Analysis has shown to be a successful alternative to the Finite Element Method (FEM). However, solving the resulting linear systems of equations efficiently remains a challenging task. In this paper, we consider a p-multigrid method, in which coarsening is applied in the spline degree p instead of the mesh width h, and...

Finding fast yet accurate numerical solutions to the Helmholtz equation remains a challenging task. The pollution error (i.e. the discrepancy between the numerical and analytical wave number k) requires the mesh resolution to be kept fine enough to obtain accurate solutions. A recent study showed that the use of Isogeometric Analysis (IgA) for the...

Isogeometric Analysis (IgA) can be considered as the natural extension of the Finite Element Method (FEM) to high-order B-spline basis functions. The development of efficient solvers for discretizations arising in IgA is a challenging task, as most (standard) iterative solvers have a detoriating performance for increasing values of the approximatio...

Wrinkling or pattern formation of thin (floating) membranes is a phenomenon governed by buckling instabilities of the membrane. For (post-) buckling analysis, arc-length or continuation methods are often used with a priori applied perturbations in order to avoid passing bifurcation points when traversing the equilibrium paths. The shape and magnitu...

The Hodgkin-Huxley (HH) neuron is one of the most biophysically-meaningful models used in computational neuroscience today. Ironically, the model’s high experimental value is offset by its disproportional computational complexity. To such an extent that neuroscientists have either resorted to simpler models, losing precious neuron detail, or to usi...

This paper introduces a new cross-platform programming framework for developing quantum-accelerated scientific computing applications and executing them on most of today’s cloud-based quantum computers and simulators. It makes use of C++ template meta-programming techniques to implement quantum algorithms as generic, platform-independent expression...

The Material Point Method (MPM) is a numerical technique that combines a fixed Eulerian background grid and Lagrangian point masses to simulate materials which undergo large deformations. Within the original MPM, discontinuous gradients of the piecewise-linear basis functions lead to the so-called grid-crossing errors when particles cross element b...

In this work, we consider a Cahn–Hilliard phase field-based computational model for immiscible and incompressible two-component liquid flows with interfacial phenomena. This diffuse-interface complex-fluid model is given by the incompressible Navier–Stokes–Cahn–Hilliard (NSCH) equations. The coupling of the flow and phase field equations is given b...

Isogeometric analysis was applied very successfully to many problem classes like linear elasticity, heat transfer and incompressible flow problems but its application to compressible flows is very rare. However, its ability to accurately represent complex geometries used in industrial applications makes IGA a suitable tool for the analysis of compr...

This work extends the high-resolution isogeometric analysis approach established in chapter “High-Order Isogeometric Methods for Compressible Flows. I: Scalar Conservation Laws” (Jaeschke and Möller: High-order isogeometric methods for compressible flows. I. Scalar conservation Laws. In: Proceedings of the 19th International Conference on Finite El...

Computational neuroscience uses models to study the brain.
The Hodgkin-Huxley (HH) model, and its extensions, is one of
the most powerful, biophysically meaningful models
currently used. The high experimental value of the (extended)
Hodgkin-Huxley (eHH) models comes at the cost of steep
computational requirements. Consequently, for larger
networks,...

Both the material-point method (MPM) and optimal transportation meshfree (OTM) method have been developed to efficiently solve partial differential equations that are based on the conservation laws from continuum mechanics. However, the methods are derived in a different fashion and have been studied independently of one another. In this paper, we...

This paper proposes a shape optimization algorithm based on the principles of Isogeometric Analysis (IGA) in which the parameterization of the geometry enters the problem formulation as an additional PDE-constraint. Inspired by the isoparametric principle of IGA, the parameterization and the governing state equation are treated using the same numer...

This paper presents a PDE-based planar parameterization framework with support for Truncated Hierarchical B-Splines (THB-splines). For this, we adopt the a posteriori refinement strategy of Dual Weighted Residual and present several adaptive numerical schemes for the purpose of approximating an inversely harmonic geometry parameterization. Hereby,...

In finite element methods (FEMs), the accuracy of the solution cannot increase indefinitely because the round-off error increases when the number of degrees of freedom (DoFs) is large enough. This means that the accuracy that can be reached is limited. A priori information of the highest attainable accuracy is therefore of great interest. In this p...

This paper presents a novel spline-based meshing technique that allows for usage of boundary-conforming meshes for unsteady flow and temperature simulations in co-rotating twin-screw extruders. Spline-based descriptions of arbitrary screw geometries are generated using Elliptic Grid Generation. They are evaluated in a number of discrete points to y...

We propose a numerical scheme based on the principles of Isogeometric Analysis (IgA) for a geometrical pattern formation induced evolution of manifolds. The development is modelled by the use of the Gray-Scott equations for pattern formation in combination with an equation for the displacement of the manifold. The method forms an alternative to the...

This paper presents a novel spline-based meshing technique that allows for usage of boundary-conforming meshes for unsteady flow and temperature simulations in co-rotating twin-screw extruders. Spline-based descriptions of arbitrary screw geometries are generated using Elliptic Grid Generation. They are evaluated in a number of discrete points to y...

The first step towards applying isogeometric analysis techniques to solve PDE problems on a given domain consists in generating an analysis-suitable mapping operator between parametric and physical domains with one or several patches from no more than a description of the boundary contours of the physical domain. A subclass of the multitude of the...

Within the original Material Point Method (MPM), discontinuous gradients of the piece-wise linear basis functions lead to so-called `grid-crossing errors' when particles cross element boundaries. This can be overcome by using $C^1$-continuous basis functions such as higher-order B-splines. In this paper, we extend this approach to unstructured tria...

The development of practical quantum computers that can be used to solve real-world problems is in full swing driven by the ambitious expectation that quantum supremacy will be able to outperform classical super-computers. Like with any emerging compute technology, it needs early adopters in the scientific computing community to identify problems o...

The paper shows a moving least squares reconstruction technique applied to the B-spline Material Point Method (B-spline MPM). It has been shown previously that B-spline MPM can reduce grid-crossing errors inherent in the original Material Point Method. However, in the large deformation regime where the grid crossing occurs more frequently, the conv...

Over the years, Isogeometric Analysis has shown to be a successful alternative to the Finite Element Method (FEM). However, solving the resulting linear systems of equations efficiently remains a challenging task. In this paper, we consider a p-multigrid method, in which each level of the hierarchy is associated with a different approximation order...

The fully automated generation of computational meshes for twin-screw machine geometries constitutes a mandatory aspect for the numerical simulation (and shape-optimization) of these devices but proves to be a challenging task in practice. Therefore, the successful generation of computational meshes requires sophisticated mathematical tools. Commer...

This paper reports on the current status of an isogeometric modeling and analysis framework for rotary twin-screw machines that is being developed by an international consortium of academic partners within the EU-funded MOTOR project. The approach aims at combining accurate geometry modeling capabilities with modern high-performance computing techn...

Isogeometric analysis was applied very successfully to many problem classes like linear elasticity, heat transfer and incompressible flow problems but its application to compressible flows is very rare. However, its ability to accurately represent complex geometries used in industrial applications makes IGA a suitable tool for the analysis of compr...

This work extends the high-resolution isogeometric analysis approach established for scalar transport equations to the equations of gas dynamics. The group finite element formulation is adopted to obtain an efficient assembly procedure for the standard Galerkin approximation, which is stabilized by adding artificial viscosities proportional to the...

High-performance computing platforms are becoming more and more heterogeneous, which makes it very difficult for researchers and scientific software developers to keep up with the rapid changes on the hardware market. In this paper, the open-source project FDBB (Fluid Dynamics Building Blocks) is presented, which eases the development of fluid dyna...

Within the standard Material Point Method (MPM), the spatial errors are partially caused by the direct mapping of material‐point data to the background grid. In order to reduce these errors, we introduced a novel technique that combines the Least Squares method with the Taylor basis functions, called Taylor Least Squares (TLS), to reconstruct funct...

A generic particle-mesh method using a hybridized discontinuous Galerkin (HDG) framework is presented and validated for the solution of the incompressible Navier-Stokes equations. Building upon particle-in-cell concepts, the method is formulated in terms of an operator splitting technique in which Lagrangian particles are used to discretize an adve...

The generation of an analysis-suitable computational grid from a description of no more than its boundaries is a common problem in numerical analysis. Most classical meshing techniques for finite-volume, finite-difference or finite-element applications such as the Advancing Front Method (Schöberl, 1997), Delaunay Triangulation (Triangle, 1996) and...