KAUST International Research Conference on Multi-Grid and Multi-Scale Methods in Computational Science, IMG 2025
ABOUT THE CONFERENCE
The International Conference on Multigrid and Multiscale Methods in Computational Science (IMG) 2025 offers a dynamic forum for researchers to share advances in Multigrid, multilevel and Multiscale computational techniques, as well as their applications across scientific domains.
Initially launched as the European Multigrid Conference (EMG), this event expanded globally in 2016, evolving into the IMG series. Since the inaugural conference in Cologne in 1981—the first event dedicated to Multigrid methods—it has driven innovation and fostered international collaboration, with notable gatherings in cities such as Amsterdam, Stuttgart, Leuven, and, most recently, Lugano.
Conference Topics:
- Multigrid Methods
- Algebraic Multigrid
- Multilevel and Multigraph Methods
- Multiscale Methods
- Domain Decomposition Methods
- Parallel and High-Performance Computing
- Software and Tools
- Computational Fluid Dynamics
- Flow and Transport in Porous Media
- Computational Finance
- Additional Applications Across Scientific Domains
AGENDA
SPEAKERS
Raimund Bürger
University of Concepción
Raimund Bürger
Models and Numerical Methods for Unit Operations in Mineral Processing and Wastewater Treatment
This presentation provides an overview and some recent developments and
mathematical problems related to models that describe unit operations in mineral
processing and wastewater treatment. The applications reviewed give rise to
multiphase flows with one or more disperse phases of small solid particles or gas
bubbles dispersed in a viscous fluid (continuous phase). The phases usually segregate
under the application of a body force, and may be composed of several components
that undergo chemical reactions. In one space dimension the governing models are
convection-diNusion-reaction partial diNerential equations partly with discontinuous
coeNicients and strong hyperbolic-parabolic type degeneracy.
After an introduction to the background of models and applications, we first review the
theory and applications of models of polydisperse solid-liquid suspensions that involve
particles diNering in size or density. These models give rise to first-order systems of
nonlinear conservation laws of arbitrary size whose velocity functions, and therefore
fluxes, are constructed in a certain systematic way. By appealing to the so-called
secular equation, a theorem on the separation of poles of rational functions, it is
possible to prove that these models are strictly hyperbolic, and the interlacing of
(known) velocity functions with (unknown) eigenvalues of the Jacobian matrix makes
spectral weighted essentially non-oscillatory (WENO) high-order schemes feasible. In
recent work versions of WENO schemes have been equipped with suitable limiters so
that they provably satisfy an invariant region principle, i.e., species volume fractions are
nonnegative and sum up to one.
A second part of the talk will review some recent developments for models of flotation
columns, which are widely used equipment for the separation of (hydrophobic)
valuable ores from (hydrophilic) gangue particles, where the former attach to the
surface of injected air bubbles, which float and eventually form the desired product,
namely foam (froth) that is collected for further processing. The operation of such a
column, including the eNect of liquid drainage through the froth, can be described by a
triangular system of convection-diNusion-reaction equations with spatially
discontinuous flux. The well-posedness analysis, invariant-region-preserving
schemes, and applications such as the construction of operating charts for this kind of
models are addressed.
Shihua Gong
The Chinese University of Hong Kong, Shenzhen
Shihua Gong
Power contractivity for RAS-Imp and RAS-PML for the Helmholtz equation
We consider two variants of restricted overlapping Schwarz methods for the Helmholtz equation. The first method, known as RAS-Imp, incorporates impedance boundary condition to formulate the local problems. The second method, RAS-PML, employs local perfectly matched layers (PML). These methods combine the local solutions additively with a partition of unity. We have shown that RAS-Imp has power contractivity for strip domain decompositions. More recently, we shown that RAS-PML has super-algebraic convergence with respective to wavenumber after a specified number of iterations. In this talk we review these results and then investigate their sharpness using numerical experiments. We also investigate situations not covered by the theory. In particular, the theory needs the overlap of the domains or the PML widths to be independent of k. We present numerical experiments where this distances decrease with k. This is a joint work with Jeffrey Galkowski, Ivan Graham, David Lafontaine and Euan Spence.
Alexander Heinlein
Delft University of Technology
Alexandar Heinlein
Not Available
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Volker John
Polytechnic of Turin (Politecnico di Torino), Italy
Volker John
Finite element methods respecting the discrete maximum principle for
convection-diffusion equations
This talk presents a survey on finite element methods, with a main focus on the convection-dominated regime of the steady-state problem, that satisfy a local or a global DMP. It reveals that for the steady-state problem there are only a few discretizations, all of them
nonlinear, that at the same time satisfy the DMPs and compute reasonably accurate solutions, e.g., algebraically stabilized schemes. Moreover, most of these discretizations have been developed in recent years, showing the enormous progress that has been achieved lately. A brief discussion of the evolutionary problem will be provided as well.
This talk is joint work with Gabriel R. Barrenechea (Glasgow) and Petr Knobloch (Prague).
Svetozar Margenov
Bulgarian Academy of Sciences, Sofia
Svetozar Margenov
Algebraic multilevel preconditioning in fractional diffusion problems
The numerical solution of spectral fractional diffusion elliptic problems is discussed. The finite element method is used for discretization. The resulting fractional degree matrix is dense, positive definite, and symmetric with respect to the inner product associated with the mass matrix. In this formulation, we apply the framework of the BURA (Best Uniform Rational Approximation) method. The BURA method of degree k reduces the nonlocal problem to solving k systems with sparse matrices. The solver for these auxiliary diffusion reaction systems plays a key role in computational efficiency.
We integrate the AMLI (Algebraic Multilevel Iteration) method into the structure of BURA and call the resulting composite method BURA-AMLI. The construction of AMLI is based on two-level recursive hierarchical block representations. The constant in the strengthened CBS (Cauchy-Buniakowski-Schwartz) inequality controls the relative condition number of the corresponding two-level and multilevel preconditioners. A key issue here is the robustness of the estimates with respect to the reaction parameters. Optimality conditions for the AMLI preconditioners are derived for the considered uniform and local mesh refinements. Thus, we obtain near-optimal estimates of the computational complexity of the BURA-AMLI algorithm.
The application of BURA in the preconditioning of coupled multiscale and multiphysics problems is discussed in the final part of the talk. Results of 2D and 3D numerical tests for the nonoverlapping domain decomposition method DD-BURA are shown. Here the Schur complement is approximated by the square root of the Laplace-Beltrami operator at the interface. The relative condition number of DD-BURA is uniformly bounded.
Kees Oosterlee
Centrum Wiskunde & Informatica, Utrecht
Kees Oosterlee
AIDA: an Analytic Isolation and Distance-based two-level Anomaly detection algorithm
In this presentation, we'll discuss anomaly detection and anomaly explanation, which is an important topic in anti-money laundering and also in fraud detection.
Many unsupervised anomaly detection algorithms rely on the concept of nearest neighbours to compute the anomaly scores. Such algorithms are popular because there are no assumptions on the data, making them a robust choice for unstructured datasets. Unfortunately, the number (k) of nearest neighbours, which critically affects the model performance, cannot be tuned in an unsupervised setting. Hence, we propose a new and parameter-free two-level Analytic Isolation and Distance-based Anomaly (AIDA) detection algorithm, that combines the metrics of distance with isolation. The distance metrics may be interpreted as a coarse level on which our anomaly detection will take place.
Based on AIDA, we also introduce the Tempered Isolation-based eXplanation (TIX) algorithm, which identifies the most relevant features characterizing an outlier, even in large multi-dimensional datasets, improving the overall explainability of the detection mechanism. Both AIDA and TIX are thoroughly tested and compared with state-of-the-art alternatives, proving to be useful additions to the existing set of tools in anomaly detection.
Gillian Queisser
University of Pennsylvania, Philadelphia
Gillian Queisser
Multiscale modeling and simulation of bacterial biofilms under antibiotic treatment
A biofilm is a community of microorganisms adhered to a surface, bound together by extracellular polymeric substances (EPS). They are ubiquitous in nature and develop on a range of surfaces both artificial and natural. Biofilms themselves typically do not negatively affect their host environment, but under certain circumstances they can retain pathogenic features and cause a wide range of medical maladies including persistent or chronic infections. In this study, we focussed on the bacterium Enterococcus faecalis. Enterococcus faecalis is a gram-positive, ubiquitous commensal bacterium commonly found in the human gastrointestinal tract. Generally, commensal E. faecalis is not a concern as it contains no mobile genetic elements, but pathogenic strains have been found to acquire mobile genetic elements including plasmids. In particular, the pCF10 plasmid confers resistance to the antibiotic erythromycin. When forming a biofilm, E. faecalis with the pCF10 plasmid constructs small complex structures with variable cellular packing. In this study, we carried out biological experiments which show that E. faecalis biofilms undergo a rapid reconfiguration of its initial architecture resulting in a doubling of cellular population over a single hour of antibiotic treatment time. We then developed a mathematical multiscale model calibrated at the micro-scale to image processing results to determine the characteristics of biofilm spatial architecture that enable the rapid one-hour reconfiguration of Enterococcus faecalis biofilm with the pCF10 plasmid under erythromycin treatment. Further, numerical simulations of our model indicate that survival requires both complex initial structures and an associated extracellular DNA (eDNA) cloud. These findings highlight the fundamental role of biofilm heterogeneity with an associated eDNA cloud in erythromycin resistance of E. faecalis with the pCF10 plasmid, and they point to the removal of eDNA as a possible avenue to increase the susceptibility of the biofilm to erythromycin.
Christoph Reisinger
University of Oxford
Christoph Reisinger
Sparse grid multilevel simulation and homogenisation for Zakai SPDEs
We analyse the accuracy and computational complexity of estimators for expected functionals of the solution to multi-dimensional parabolic stochastic partial differential equations (SPDE) of Zakai-type. These equations may arise as large pool models of equity and credit markets. We consider a Milstein scheme for time integration and an alternating direction implicit (ADI) splitting of the spatial finite difference discretisation, coupled with the sparse grid combination technique and multilevel Monte Carlo sampling (MLMC). In the two-dimensional case, we find by detailed Fourier analysis that the work complexity of MLMC on sparse grids has the optimal power law behaviour of order -2 in the root-mean-square error (RMSE). Numerical tests confirm these findings empirically. We give a discussion of the higher-dimensional setting without detailed proofs. Furthermore, we study a two-dimensional Zakai equation that includes a fast mean-reverting stochastic volatility component and construct a heuristic expansion in the small mean-reversion parameter. We verify numerically for the first two terms weak convergence order half and order one, respectively, in the mean-reversion parameter. To this end, we give a numerical scheme for the original two-dimensional SPDE, which is robust in the small parameter regime, and compare derived functionals of marginals against those approximated by the solution of a sequence of one-dimensional SPDEs with coefficients averaged over the ergodic distribution. The first part is based on joint work with Zhenru Wang, the second part additionally with Sam Howison and Ronnie Sircar.
Kees Vuik
Delft University of Technology
Kees Vuik
Resolving Divergence: The First Multigrid Scheme for the Highly Indefinite Helmholtz Equation Using Classical Components
In this talk, we present the first stand-alone classical multigrid solver for the highly in-
definite 2D Helmholtz equation with constant costs per iteration, addressing a longstanding open problem in numerical analysis [1]. Our work covers both large constant and non-constant wavenumbers up to k = 500 in 2D.
We obtain a full V − and W−cycle without any level-dependent restrictions. Another
powerful feature is that it can be combined with the computationally cheap weighted Jacobi smoother. The key novelty lies in the use of higher-order inter-grid transfer operators [2]. When combined with coarsening on the Complex Shifted Laplacian, rather than the original Helmholtz operator, our solver is h−independent and scales linearly with the wavenumber k. If we use GMRES(3) smoothing we obtain k− independent convergence, and can coarsen on the original Helmholtz operator, as long as the higher-order transfer operators are used. This work opens doors to study robustness of contemporary solvers, such as machine learning solvers inspired by multigrid components, without adding to the black-box com-plexity.
Alfo Grillo
Polytechnic of Turin Alfo Grillo
Not Available
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Markus Knodel
Simulation in TechnologyMarkus Knodel
An efficient algorithm for biomechanical problems based on a fully implicit nested Newton solver
We provide a novel algorithmic strategy to efficiently compute the dynamics of soft biological tissues. In this respect, numerical simulations of such physical systems are highly non-trivial because tissues generally exhibit complex biological response to external or internal actions, including large deformations and remodelling. The proposed algorithm, named BioMechanics Basis Plasticity Algorithm (BMBPA), is fully implicit and based on a nested Newton solver.
According to the formulation provided in this work, the BMBPA can be easily employed to
solve several types of biological and biomechanical problems, since it asks for very few condition for being applied. Moreover, we show that the performances of BMBPA are substantially higher than those of another computational algorithm taken from the literature and known as General Plasticity Algorithm (GPA). In particular, we put in evidence how the BMBPA is able of solving the deformation and the remodeling of biological tissues by employing a computation time of hours, while the GPA, applied to the same problems as the BMBPA, may be unable of returning solutions within a time window of months. Finally, we also display the characteristic of BMBPA of being parallelized, a property which does not belong to the GPA.
To test the BMBPA and to compare it to the GPA, we consider two sets of simulations in
which specific benchmark tests are simulated and numerically solved. In one case, we consider the shear-compression test of a cubic specimen of tissue, while, in the other case, we focus on the unconfined compression test of a cylinder. In both situations, we emply a monophasic model of a fibre-reinforced tissue, representing e.g. articular cartilage. The Bilby-Kröner-Lee (BKL) multiplicative decomposition of the deformation gradient tensor is employed to introduce the unknowns of our model. In particular, we distinguish between global and local unknowns, associated with local and global equations, respectively, and connected by means of a resolution function. The results of our simulations permit to study the overall mechanical behavior of the considered tissue quantitatively determine the efficiency of the BMBPA and its versatility in being used in the field of tissue Biomechanics.
Intracellular "in silico microscopes" - fully 3D spatio-temporal virus replication model simulations
Despite being small and simple structured in comparison to their victims, virus particles have the potential to harm severly and even kill highly developed species such as humans. To face upcoming virus pandemics, detailed quantitative biophysical understanding of intracellular virus replication mechanisms is crucial. Unveiling the relationship of form and function will allow to determine putative attack points relevant for the systematic development of direct antiviral agents (DAA) and potent vaccines. Biophysical investigations of spatio-temporal dynamics of intracellular virus replication so far are rare.
We are developing a framework to allow for fully spatio-temporally resolved virus replication dynamics simulations based on partial differential equation models (PDE) and evaluated with advanced numerical methods on large supercomputers. This study presents an advanced highly nonlinear model of the genome replication cycle of a specific RNA virus, the Hepatitis C virus (HCV). The diffusion-reaction model mimics the interplay of the major components of the viral RNA (VRNA) cycle, namely non structural viral proteins (NSP), VRNA and a generic host factor (energy supply etc.). Technically, we couple surface PDEs (sufPDEs) on the 3D embedded 2D Endoplasmatic Reticulum (ER) manifold with PDEs in the 3D membranous web (MW) and cytosol volume. (The MWs are the replication factories growing on the ER induced by NSPs.) The sufPDE/PDE model is evaluated at realistic reconstructed cell geometries which are based on experimental data. The simulations couple the effects of NSPs which are restricted to the ER surface with effects appearing in the volume. The volume effects include the host factor supply from the cytosol and the MW dynamics. Special emphasis is put to the exchange of components between ER surface, MWs and cytosol volume. As the vRNA spatial properties are not fully understood so far in experiment, the model allows for vRNA both restricted to the ER and moving in the cytosol. The visualization of the simulation resembles a look into some sort of fully 3D resolved "in silico microscopes" to mirror and complement in vitro /in vivo experiments for the intracellular VRNA cycle dynamics. The output data are quantitatively consistent with experimental data and provoke advanced experimental studies to validate the model.
Stephan Matthai
The University of Melbourne Stephan Matthai
Influence of inertial and centrifugal forces on rate and flow patterns in natural fracture networks
Simple mass balance calculations indicate that fluid injection or production of fractured rocks in the subsurface induces flow velocities of meters per second. However, most engineering approaches still treat flow through fractured rock masses as laminar creeping flow or approximate inertia effects by tuning constitutive relationships determined for single fractures. Here we consider this problem for entire networks of intersecting mm-wide up to 20-m long natural fractures as seen in outcrops of brittle rocks. Thousands of fractures are resolved by a collocated 2D discrete-fracture finite element – finite volume mesh. Simulations solve the Reynolds-time-averaged Navier Stokes equations blending a purely viscous with the K - approach, investigating the transition from laminar creeping to turbulent flow as fluid-throughput increases. Flow patterns and spatial velocity variations are presented considering water as an example of a Newtonian fluid. This analysis of flow regimes and velocities rests on a model verification for an idealized fracture intersection. Our results show that for fracture flow velocities greater than ∼1-cm/s, fluid inertia begins to markedly alter flow patterns and the velocity distribution in the network. At higher velocities we even see flow direction reversals in some of the smaller fractures as compared with laminar creeping flow. For any fluid throughput Reynold’s number varies across the networks by many orders of magnitude, following multi-modal distributions. We conclude that, for fracture networks, the relationship between the applied far-field pressure gradient and fluid throughput becomes non-linear long before single fractures enter the so-called “weak inertia” regime. This prominence of inertia effects and accompanying changes of flow patterns and transport highlights the need to improve network-scale flow models for the benefit of engineering applications like fracture stimulation, hydrocarbon recovery, geothermal energy extraction, gas storage and groundwater abstraction
Niklas Conen
Goethe University Frankfurt
Niklas Conen
Not Available
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Peter Frolkovic
Slovak University Of Technology Peter Frolkovic
High resolution implicit discretizations for advection dominated PDEs with multiple time scales
We present novel implicit high resolution time discretization method for hyperbolic problems that contain processes with multiple time scales. The method has unconditional stability, so the choice of time steps is driven only by accuracy requirements. The method can be used to solve advection dominated PDEs. The method has higher order accuracy for smooth parts of solutions and non-oscillatory behavior near steep gradients or shocks. It exhibits compact stencils that enable fast solvers for resulting algebraic systems of equations. Numerical experiments include shallow water equations with topography and level set methods for tracking dynamic interfaces including two-scales models of dissolution and precipitation of minerals in groundwater flows .
Olaf Steinbach
TU Graz Olaf Steinbach
Optimal complexity solution of space-time finite element systems for state-based parabolic distributed optimal control problems
In this lecture we consider a distributed optimal control problem subject to a parabolic evolution equation as constraint. The approach presented here is based on the variational formulation of the parabolic evolution equation in anisotropic Sobolev spaces, considering the control in $[H_{0;,0}^{1,1/2}(Q)]^*$. The state equation then defines an isomorphism onto $H^{1,1/2}_{0;0,}(Q)$, where the anisotropic Sobolev norm can be realized by using a modified Hilbert transformation. As in the classical approach we consider the associated optimality system from which we can eliminate both the adjoint state and the control. After discretization, the cost or regularization term involves a Schur complement matrix $S_h = B_h^\top A_h^{-1} B_h$, defining a norm on the state space, with $B_h$ being the space-time finite element matrix for the parabolic evolution equation, and $A_h^{-1}$ representing the norm for the control. While the structure of the Schur complement matrix $S_h$ may complicate an efficient numerical solution of the discrete optimality system, instead of $S_h$ we use a spectrally equivalent matrix $D_h$ which also defines a norm on the state space, but allows a more efficient realization. Moreover, using a space-time tensor product mesh, we can use sparse factorization techniques to construct a solver of almost linear complexity.
Alfio Borzi
University of WuerzburgSabine Le Borne
Hamburg University of TechnologySabine Le Borne
Coupled ordering techniques for coupled systems of partial differential equations - coupled clustering in hierarchical matrices
The discretization of coupled systems of partial differential equations typically leads to discrete systems of equations with a block structure that exhibits the different types of unknowns. An example is given by the Navier-Stokes equations which models velocity and pressure of a fluid in a certain spatial domain.
These systems of equations are typically very large and need to be solved iteratively. The performance of iterative solvers often depends on the ordering of the degrees of freedom. In the past, orderings have often been discussed separately for the different types of unknowns.
In this talk, we discuss coupled ordering techniques for the pressure and velocity unknowns of the linearized Navier-Stokes equations that facilitate the computation of subsequent Schur complement approximations in typical block preconditioners. In particular, such orderings can be combined with block clustering strategies in the construction of hierarchical matrices and accelerate the construction of hierarchical LU factorizations of the Schur complement. Numerical results illustrate the performance of the resulting saddle point
preconditioners.
Steffen Börm
University of Kiel Steffen Börm
Adaptive H²-matrix multiplication
H²-matrices provide us with efficient approximations of matrices arising as solution operators of elliptic partial differential equations or integral operators. Their main advantage is that they have linear complexity with respect to storage requirements and certain arithmetic operations.
Approximating the product of two H²-matrices has proven to be a major challenge for years, since it requires us to take interactions between different levels of the discretization into account. In this presentation, we discuss an algorithm that allows us to approximate the product in linear complexity while guaranteeing a given accuracy for the result.
In a first phase, the algorithm finds an exact representation of the product using a refined block structure. In the second and third phases, this representation is approximated by the given H²-matrix structure.
Ulrich Langer
Johannes Kepler University Linz Ulrich Langer
Robust space-time finite element solvers for distributed hyperbolic optimal control problems
We propose, analyze, and test new robust iterative solvers for systems of linear algebraic equations arising from the space-time finite element (fe)discretization of reduced optimality systems defining the approximate solution of hyperbolic distributed, tracking-type optimal control problems with both the standard $L^2$ and the more general energy regularizations.
In contrast to the usual time-stepping approach, we discretize the optimality system by space-time continuous piecewise-linear fe basis functions which are defined on fully unstructured simplicial meshes. If we aim at the asymptotically best approximation of the given desired state $y_d$ by the computed fe state $y_{\varrho h}$, then the optimal choice of the regularization parameter $\varrho$ is linked to the space-time fe mesh-size $h$ by the relations $\varrho=h^4$ and $\varrho=h^2$ for the $L^2$ and the energy regularization, respectively. For this setting, we can construct robust (parallel) iterative solvers for the reduced fe optimality systems.In practice, we use these solvers in a nested iteration framework that allows us to control the accuracy of the state iterates and the cost of the control in a systematic way on a sequence of uniformly or adaptively refined meshes.
In the case of adaptively refined meshes, we may use variable regularization parameters adapted to the local behavior of the mesh-size. The numerical results illustrate the theoretical findings firmly.
Lech Grzelak
Utrecht UniversityLech Grzelak
Beyond affine models: On inclusion of random parameters in pricing models
In this talk, we challenge the traditional reliance on Affine (Jump) Diffusion (AD) models in financial pricing through the introduction of Randomized AD (RAnD) models. By integrating exogenous stochasticity into model parameters, RAnD extends beyond the limitations of affine models, offering enhanced flexibility and precision in option pricing. This approach not only overcomes the linearity constraints of AD models but also maintains the benefits of quick calibration and efficient Monte Carlo simulations. We explore the theoretical foundations and practical implementations of RAnD, including the derivation of characteristic functions, simulation techniques, and sensitivity analysis. Specifically, we demonstrate the superiority of randomized stochastic volatility models through the consistent pricing of options on the S&P 500 and VIX. Furthermore, we extend our investigation to short-rate models within the Heath-Jarrow-Morton framework, applying RAnD to achieve controlled implied volatility and improved calibration quality. The randomized HullWhite model exemplifies the potential of RAnD in producing local volatility dynamics and achieving near-perfect calibration to swaption implied volatilities. This talk underscores the significance of incorporating random parameters into pricing models, marking a departure from traditional affine models towards a more nuanced and practical modelling approach in financial markets.
Matthieu Meunier
University of Oxford Matthieu Meunier
Multilevel Picard Iteration in the Numerical Approximation of Entropy-Regularized Markov Decision Processes
Many optimization problems in finance can be effectively modeled using Markov Decision Processes. However, estimating the optimal Q-function is often intractable due to the curse of dimensionality. In this work, we address this challenge in the context of entropy-regularized MDPs, where the addition of a relative entropy term incentivizes exploration and facilitates theoretical analysis. We introduce a novel estimator for approximating the optimal Q-function for MDPs with arbitrary state and action spaces. The estimator is based on Picard iterations combined with multilevel Monte Carlo techniques, offering a flexible framework for approximating the Bellman operator. We investigate two implementations: the first is based on a biased Monte Carlo sample average and the second relies on an unbiased estimator by Blanchet and Glynn (2015). We show that the latter effectively breaks the curse of dimensionality, establishing the first such result in Polish action and state spaces. We perform a rigorous analysis of the estimator’s error and computational complexity in its general and specialized forms. Finally, we revisit a classical financial application with our new estimator.
Marco Donatelli
University of Insubria, Italy Marco Donatelli
Matrices associated to two conservative discretizations of Riesz fractional operators and related multigrid solvers
We focus on a two-dimensional conservative steady-state Riesz fractional diffusion problem, discretized using finite volume methods. We analyze the spectrum of the associated matrices and propose efficient multigrid preconditioners.
Junxi Wang
Junxi Wang
Multiscale Diffusion Simulation in UG4: from Nanostructure of Lipid Molecules to Stratum Corneum
The stratum corneum (SC) layer, the outermost layer of skin, has attracted considerable interest in the field of pharmacy due to its pivotal role in transdermal drug delivery. Numerous mathematical models have been developed based on the microstructure of the SC layer, which is regarded as a periodic arrangement of hydrophilic corneocytes embedded in an hydrophobic lipid matrix.The substance permeabilities are distinguished by their relative hydrophilicities to these two phases.
However, the validity of research conducted on these two phases has been called into question as the nanostructure of the lipid matrix is discovered in greater detail. Fortunately, there has been an increase in the number of scientists attempting to understand the diffusion process in the lipid matrix. For instance, molecular dynamics can be used to continuously explain substance permeabilities in a lipid biliayer.
Nevertheless, it will require significant running time and memory to conducte such simulations with nanoscale parameters on a macroscale area. To address this challenge, this study employs a multiscale simulation approach, leveraging the homogenization method to bridge the parameters from the lower scale to the next larger one while maintaining the size of the larger scale simulation constant.
Ralf Kornhuber
Freie Universität Berlin Ralf Kornhuber
Not Available
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Mini-Symposium Speakers, and Contributed Lectures
Mariam Almudarra
Multi-Scale Analysis of Avascular Tumour Growth: A Variable-Order Non-Local ApproachAndrea Borio
Recent advancements in polygonal methods: stabilization-free Virtual Element MethodsAnnachiara Colombi
Non-local multi-scale model for Cancer-on-Chip experiments: a two-step global sensitivity analysisLuca Lussardi
Variational analysis of nematic axisymmetric filmsAlberto Girelli
Multiscale modelling of fluid flow in a lymph nodePatrick Zulian
An immersed method for fluid-structure-contact interactionAlena Kopanicakova
Operator-learning based preconditioning strategiesMarco Favino
Fractures and thin heterogeneities as Robin-Wentzell interface conditionsLuca Franco Pavarino
Parallel Algebraic Multigrid Solvers for Composite Discontinuous Galerkin Discretization of the Cardiac EMI Model in Heterogeneous MediaKen Trotti
Additively Preconditioned Trust Region Strategies for Machine LearningHardik Kothari
Integrating Additive Multigrid with Multipreconditioned Conjugate Gradient MethodPietro Benedusi
Scalable approximation and solvers for ionic electrodiffusion in cellular geometriesArne Nägel
Computational Methods and Efficient Solvers for Non-linear ProblemsDmitry Logashenko
Multilevel Monte Carlo Method for Estimation of Uncertainties in Fractured Porous MediaElsa Nicole Flores Pretell
A Brief Proposal for a PDE-based Morphodynamic Model of Neuronal Growth Cone DynamicsEmma Perracchione
Dimensionality reduction via optimal kernel designAndrea Pastore
Internal Constraints and Gauge Relations in the Theory of Uniaxial Nematic ElastomersNicolas Neuss
Simulation of the transport of superparamagnetic nanoparticles under the influence of an magnetic fieldAndrea Angino
Two-level trust-region method with random subspacesJohannes Benedikt Schröter
Modeling Soil Microbial Dynamics: Application of aGeneralized Lotka-Volterra Model to Soil MicrobiomeTime Series DataTobias Weinzierl
Task-based implementations of advanced multigrid solvers for Discontinuous Galerkin methodsMohammed Al Kobaisi
A Sparsified Multiscale (SM) Preconditioner for fractured porous mediaMatthias Bolten
Aggregation and block smoothers in symbol-based multigrid methods for block Toeplitz systemsMohamed DALAH
MATLAB Implementation of a Multigrid Solver for Diffusion-Wave EquationsJulian Hilbert
Iterative Coupling Approach for Time-Step-Constrained Models Using UG4Martin Parnet
Study of Time-Parallel Method solving method for the quasi-static Biot equationFabio Credali
The reduced basis multigrid scheme for the virtual element methodShahad Almatrafi
Multi-Scale Modeling of Protein Dynamics and Evolution in Disease-Related MutationsMuhammad Shahid Ashraf
Multigrid Methods for Singularly Perturbed Reaction-Diffusion Equations on Complex GeometriesHisham bin Zubair Syed
Multigrid for Fourth order Partial Differential Equations: Components, and their AnalysisXiaofeng Xu
Randomized greedy algorithms for neural network optimizationJongho Park Park
Universal coarse spaces for various finite element discretizations of $2m$th-order elliptic problemsJindong Wang
A robust solver for H(curl) convection-diffusion and its local Fourier analysisXinliang Liu
Neural Networks and Operators Based on Convolution and Multigrid StructureTong Mao
Expressivity and Approximation Properties of Deep Neural Networks with ReLUk ActivationXianlin Jin
An adaptive greedy algorithm with hierachical basis for solving elliptic equationQijia Zhai
Is the Frequency Principle always valid?ORGANIZERS Committee
Martin Gander
University of Geneva
Alfio Grillo
Politecnico di Torino
Rolf Krause
(Chair), KAUST
Zeyao Mo
Peking University, Beijing
Arne Nägel
Goethe University Frankfurt
Gillian Queisser
University of Pennsylvania, Philadelphia
Arnold Reusken,
RWTH Aachen University
Jacob Schroder
Sandia National Laboratories, Albuquerque
Volker Schulz
University of Trier
Gabriel Wittum
KAUST
Jinchao Xu
KAUST
Ulrike Meier Yang
Lawrence Livermore National Laboratory
INFORMATION
Submission Deadlines
Minisymposium Proposals Submission
Abstracts Submission
Proceedings
Accepted abstracts will be published in special issues of the International Journal of Computing and Visualization in Science and Engineering.
Conference Location
The conference will be held at King Abdullah University of Science and Technology (KAUST), located in Thuwal, Saudi Arabia. Attendees will have the opportunity to explore the world-class facilities and beautiful coastal campus of KAUST.
KAUST - Building 19, Hall 1, 2 and 3
Excursions
As part of the conference, excursions are planned for Thursday, February 6, and Friday, February 7, 2025. These outings will offer participants a unique opportunity to experience the region’s cultural and natural landscapes.
Visa Information
Citizens of many countries are eligible to enter Saudi Arabia on a tourist visa. Please check eligibility and apply at Visit Saudi. If your country is not listed, contact the conference office for assistance with visa arrangements.
Travel
The primary airport for travel to KAUST is King Abdulaziz International Airport in Jeddah. From there, you can reach KAUST by taxi or by taking a train to King Abdullah Economic City (KAEC) and continuing by taxi.
Taxi information:
The conference will provide buses for your transportation from the KAUST hotel to the event venue.
Date | Pickup Location | Time | Frequency |
|---|---|---|---|
3-Feb-25 | Visitor Center / Al Khozama Hotel / Building 20 | 8:30 AM - 17:00 | Every 15 Minutes |
Al-Khozama Hotel / Building 20 | 8:30 AM - 10:30 AM | Every 15 Minutes | |
4-Feb-25 | Visitor Center / Al Khozama Hotel / Building 20 | 8:30 AM - 17:00 | Every 15 Minutes |
Al-Khozama Hotel / Building 20 | 8:30 AM - 10:30 AM | Every 15 Minutes | |
5-Feb-25 | Visitor Center / Al Khozama Hotel / Building 20 | 8:30 AM - 17:00 | Every 15 Minutes |
Al-Khozama Hotel / Building 20 | 8:30 AM - 10:30 AM | Every 15 Minutes |
Accommodations
Al Khozama Hotel
Located on the KAUST campus, the 5-star Al Khozama Hotel offers comfortable and convenient lodging. Bookings can be made directly [here], with a two-step process to confirm campus access.
Bay La Sun Hotel
Located in King Abdullah Economic City, Bay La Sun Hotel and Marina offers a 5-star experience with seaside views. Daily shuttle service will be provided for IMG 2025 attendees, with an estimated 30-minute commute each way, including campus access.
Registration Fee and Details
Registration is required for all participants. The conference fee includes lunches, coffee/tea breaks, a conference dinner and a collection of abstracts.
Registration Fees
- Before January 15, 2025
USD150– ParticipantsUSD100– Students- After January 16, 2025
- USD 300 – Participants
KAUST CORE LABS
KAUST CORE LABS
KAUST hosts a wide range of sophisticated instruments and world-class facilities that students can access, including the Prototyping and Product Development Core Lab, and laboratories involving robotics and embedded systems, sensors, intelligent autonomous systems and biotechnology. Specific labs will be identified based on the curriculum and individual projects.
KAUST IMPACT
KAUST Impact Summer 2024, the latest edition of the magazine.
KAUST IMPACT
A NEW ERA FOR KAUST
Our unrelenting commitment to research, innovation and talent has seen KAUST establish itself as one of the leading research universities in the world, ranking #1 for citations per faculty globally, with a reputation for impact-driven research that contributes to the betterment of the world. This new era of KAUST builds on our many successes, achievements and strong foundations, and our new strategy represents an evolution that brings us closer to the interests of the Kingdom.
CONTACT US
King Abdullah University of Science and Technology (KAUST)
4700 King Abdullah University of Science and Technology
Thuwal 23955-6900
Kingdom of Saudi Arabia
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This event is sponsored by the Office of Research Funding and Services
For any inquiries, don't hesitate to get in touch with us at img.2025@kaust.edu.sa
© 2025 King Abdullah University of Science and Technology. All rights reserved.