Allan Peter Engsig-Karup

Technical University of Denmark | DTU · Department of Applied Mathematics and Computer Science

We present a spectral element model for general-purpose simulation of non-overturning nonlinear water waves using the incompressible Navier-Stokes equations (INSE) with a free surface. The numerical implementation of the spectral element method is inspired by the related work by Engsig-Karup et al. (2016) and is based on nodal Lagrange basis functi...

We present a new high-order spectral element solution to the two-dimensional scalar Poisson equation subject to a general Robin boundary condition. The solution is based on a simplified version of the shifted boundary method employing a continuous arbitrary order hp-Galerkin spectral element method as the numerical discretization procedure. The sim...

Using high performance computing (HPC) today it is possible to use fully nonlinear potential flow (FNPF) modelsfor tasks that previously was restricted to asymptotic wave modelling, such as models based on Boussinesq-type orGreen-Nadgy equations, due to computational effort. Indeed, as shown in [11] the dispersion properties of a FNPFmodel can be t...

In outdoor acoustics, the calculations of sound propagating in air can be computationally heavy if the domain is chosen large enough for the sound waves to decay. The computational cost is lowered by strategically truncating the computational domain with an efficient boundary treatment. One commonly used boundary treatment is the perfectly matched...

Amidst recent advancements in the 3D digital representation that have significantly enhanced the modeling of geometric attributes of pre-existing environments, accurate estimation of acoustic boundary conditions remains a complex challenge. This paper presents a novel way to determine what we refer to as a neural boundary field, using physics-infor...

We propose physics-informed holomorphic neural networks (PIHNNs) as a method to solve boundary value problems where the solution can be represented via holomorphic functions. Specifically, we consider the case of plane linear elasticity and, by leveraging the Kolosov-Muskhelishvili representation of the solution in terms of holomorphic potentials,...

To improve both scale and fidelity of numerical water wave simulations to study the evolution of wave fields within offshore engineering, it is of key practical interest to achieve high numerical efficiency. We propose a p-multigrid accelerated time-domain scheme for efficient and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasys...

This paper describes a new high-order composite numerical model for simulating moored floating offshore bodies. We focus on a floating offshore wind turbine and its static equilibrium and free decay. The composite scheme models linear to weakly nonlinear motions in the time domain by solving the Cummins equations. Mooring forces are acquired from a...

Evaluating the acoustics of courtyards has gained increasing attention from a sustainable urban design perspective, which requires numerical predictions tools for estimation of noise pollution and assessment of the influence of acoustic conditions. Accurate modeling of the acoustics of a courtyard is scarce because of the variety of factors to incl...

We propose physics-informed holomorphic neural networks (PIHNNs) as a method to solve boundary value problems where the solution can be represented via holomorphic functions. Specifically, we consider the case of plane linear elasticity and, by leveraging the Kolosov-Muskhelishvili representation of the solution in terms of holomorphic potentials,...

We present a new high-order accurate computational fluid dynamics model based on the incompressible Navier-Stokes equations with a free surface for the accurate simulation of nonlinear and dispersive water waves in the time domain. The spatial discretization is based on Chebyshev polynomials in the vertical direction and a Fourier basis in the hori...

We present a general multi-fidelity (MF) framework which is applied through utilizing flexible-order explicit finite difference numerical schemes using convo-lutional neural networks (CNNs) by combining low-order simulation data with higher order simulation data obtained from numerical simulations based on partial differential equations (PDEs). Thi...

IWWWFB39 (Accepted). Source: https://sites.dundee.ac.uk/iwwwfb2024/accepted-abstracts/. We consider the setting of fully nonlinear potential flow when simulating free surface waves using finite volume/cell/element methods. Here, the fluid domain is bounded by arbitrarily complex boundaries in topology and shape but also time-dependent (deforming...

This paper presents a novel, efficient, high-order accurate, and stable spectral element-based model for computing the complete three-dimensional linear radiation and diffraction problem for floating offshore structures. We present a solution to a pseudo-impulsive formulation in the time domain, where the frequency-dependent quantities, such as add...

Submission to IWWWFB 2024 (accepted): We propose a new high-order finite difference numerical model for the simulation of nonlinear water waves and wave-structure interaction with fixed structures using the Navier-Stokes equations. The complete formulation is described in three spatial dimensions (3D) and preliminary validation results are here pre...

We address the challenge of acoustic simulations in three-dimensional (3D) virtual rooms with parametric source positions, which have applications in virtual/augmented reality, game audio, and spatial computing. The wave equation can fully describe wave phenomena such as diffraction and interference. However, conventional numerical discretization m...

Model order reduction techniques significantly reduce the computational time when performing accurate room acoustic simulations with numerical methods that inherently include all the wave phenomena. There is a clear trade-off between physical accuracy and acceleration, but how humans perceive these errors is unknown. This study aims to investigate...

We present a massively parallel and scalable nodal discontinuous Galerkin finite element method (DGFEM) solver for the time-domain linearized acoustic wave equations. The solver is implemented using the libParanumal finite element framework with extensions to handle curvilinear geometries and frequency dependent boundary conditions of relevance in...

We present a new high-order accurate spectral element solution to the two-dimensional scalar Pois-son equation subject to a general Robin boundary condition. The solution is based on a simplified version of the shifted boundary method employing a continuous arbitrary order hp-Galerkin spectral element method as the numerical discretization procedur...

Deep neural operators have seen much attention in the scientific machine learning community over the last couple of years due to their capability of efficiently learning the nonlinear operators mapping from input function spaces to output function spaces showing good generalization properties. This work will show how to set up a performant DeepONet...

We address the challenge of sound propagation simulations in $3$D virtual rooms with moving sources, which have applications in virtual/augmented reality, game audio, and spatial computing. Solutions to the wave equation can describe wave phenomena such as diffraction and interference. However, simulating them using conventional numerical discretiz...

This paper presents a novel, efficient, high-order accurate, and stable spectral element-based model for computing the complete three-dimensional linear radiation and diffraction problem for floating offshore structures. We present a solution to a pseudo-impulsive formulation in the time domain, where the frequency-dependent quantities, such as add...

Accepted conference paper for ISOPE-2023: This paper describes a new high-order composite numerical model designed for the efficient arbitrary-scale simulation of moored floating offshore bodies. The study focuses on static equilibrium and free decay of such structures, particularly a floating offshore wind turbine. The composite scheme models the...

Quick simulations for iterative evaluations of multi-design variables and boundary conditions are essential to find the optimal acoustic conditions in building design. We propose to use the reduced basis method (RBM) for realistic room acoustic scenarios where the surfaces have inhomogeneous acoustic properties, which enables quick evaluations of c...

Room acoustic simulations can be performed by means of numerical methods, which typically solve the wave equation in an enclosure using discretization techniques. These methods provide high-fidelity solvers that include all the wave phenomena but are computationally costly. This paper presents the potential of a reduced basis method for simulating...

Deep learning-based approaches in machine learning have become popular for automatically detecting defects in electroluminescence images of solar cells. However, the data available to train such models is currently a bottleneck for their performances due to expensive and possibly inaccurate labeling. To address this problem, we propose to use a mod...

Quick simulations for iterative evaluations of multi-design variables and boundary conditions are essential to find the optimal acoustic conditions in building design. We propose to use the reduced basis method (RBM) for realistic room acoustic scenarios where the surfaces have inhomogeneous acoustic properties, which enables quick evaluations of c...

We present a scalable two‐dimensional Galerkin spectral element method solution to the linearized potential flow radiation problem for wave induced forcing of a floating offshore structure. The pseudo‐impulsive formulation of the problem is solved in the time domain using a Gaussian displacement signal tailored to the discrete resolution. The added...

Simulating acoustics efficiently and accurately using numerical methods has been an active research area for the last decades and has applications in computer games, VR/AR, and architectural design. However, their extensive computation time makes these methods challenging for large scenes and broad frequency ranges. This work attempts to accelerate...

Simulating acoustics efficiently and accurately using numerical methods has been an active research area for the last decades and has applications in computer games, VR/AR, and architectural design. However, their extensive computation time makes these methods challenging for large scenes and broad frequency ranges. This work attempts to accelerate...

The use of model-based numerical simulations of wave propagation in rooms for engineering applications requires that acoustic conditions for multiple parameters are evaluated iteratively, which is computationally expensive. We present a reduced basis method (RBM) to achieve a computational cost reduction relative to a traditional full-order model (...

We propose and demonstrate a new approach for fast and accurate surrogate modelling of urban drainage system hydraulics based on physics-guided machine learning. The surrogates are trained against a limited set of simulation results from a hydrodynamic (HiFi) model. Our approach reduces simulation times by one to two orders of magnitude compared to...

We propose and demonstrate a new approach for fast and accurate surrogate modelling of urban drainage system hydraulics based on physics-guided machine learning. The surrogates are trained against a limited set of simulation results from a hydrodynamic (HiFi) model. Our approach reduces simulation times by one to two orders of magnitude compared to...

We present a scalable 2D Galerkin spectral element method solution to the linearized potential flow radiation problem for wave induced forcing of a floating offshore structure. The pseudo-impulsive formulation of the problem is solved in the time-domain using a Gaussian displacement signal tailored to the discrete resolution. The added mass and dam...

The use of epidemic modelling in connection with spread of diseases plays an important role in understanding dynamics and providing forecasts for informed analysis and decision-making. In this regard, it is crucial to quantify the effects of uncertainty in the modelling and in model-based predictions to trustfully communicate results and limitation...

Estimating the hydrodynamic characteristics of bodies interacting with ocean waves is of key importance in ocean engineering. Solving the wave-structure interaction problem has been a topic of research for many years, especially using linearized potential flow theory which generally captures the majority of the physics for typical marine structures...

No PDF available ABSTRACT The development of efficient and accurate numerical methods for simulating realistic sound in virtual environments—such as computer games and VR/AR—has been an active research area for the last decades. However, handling dynamic scenes with many moving sources is still challenging due to intractable storage requirements an...

Submitted to IWWWFB 2022. This abstract describes our recent work on employing reduced-order modelling (ROM) to solve fully nonlinear potential flow equations (FNPF) to achieve faster turn-around time than a full order model (FOM) based on the spectral element method (SEM) [1]. We propose a PODGalerkin based model-order reduction approach to reduc...

Submitted to IWWWFB 2022. Simulation of water waves and taking into account the sea floor to estimate sea states are important for the design of offshore structures. We propose a new high-order accurate pseudospectral method for solving the incompressible Navier-Stokes equations with a free surface. The work is motivated by the lack of high-order a...

Submitted to IWWWFB 2022. See the published version. Estimating the hydrodynamic characteristics of bodies interacting with ocean waves is of key importance in ocean engineering. Solving the wave-structure interaction problem has been a topic of research for many years, especially using linearized potential flow theory which generally captures th...

We present a numerical case study for modeling and simulation of upstream and downstream processes for monoclonal antibody (mAb) production. We apply a systematic and intuitive modeling methodology for an existing upstream process and downstream process. The resulting models are based on differential mass balances and kinetic expressions for the re...

Realistic sound is essential in virtual environments, such as computer games and mixed reality. Efficient and accurate numerical methods for pre-calculating acoustics have been developed over the last decade; however, pre-calculating acoustics makes handling dynamic scenes with moving sources challenging, requiring intractable memory storage. A phy...

Realistic sound is essential in virtual environments, such as computer games and mixed reality. Efficient and accurate numerical methods for pre-calculating acoustics have been developed over the last decade; however, pre-calculating acoustics makes handling dynamic scenes with moving sources challenging, requiring intractable memory storage. A phy...

During the COVID-19 pandemic, Denmark has pursued a mass testing strategy culminating in the testing of 12.167 individuals per 100,000 inhabitants per day during the spring of 2021. The strategy included free access to COVID-19 testing, and since 2021, compulsory documentation for negative tests or vaccination has been required for access to workpl...

The estimation of extreme loads from waves is an essential part of the design of offshore wind turbines. Standard design codes suggest either to use simplified methodologies based on regular waves, or to perform fully-nonlinear computations. The former may not provide an accurate representation of the real extreme waves, while the latter is too com...

In the political decision process and control of COVID-19 (and other epidemic diseases), mathematical models play an important role. It is crucial to understand and quantify the uncertainty in models and their predictions in order to take the right decisions and trustfully communicate results and limitations. We propose to do uncertainty quantifica...

During the Covid-19 pandemic, Denmark has pursued a unique mass testing strategy culminating in testing of more than 8,000 citizens per 100,000 inhabitants per day in the Spring 2021. The strategy includes free access to Covid-19 testing and since 2021, compulsory documentation for negative test or vaccination for access to workplace, educational i...

It is well known that input data uncertainty has a major influence on the correctness of room acoustic simulations. This paper proposes a comprehensive framework for experimental validation and uncertainty quantification in room acoustic simulations. The sources of uncertainty in room acoustic simulations are many, but especially the boundary condi...

We present a Spectral Element Fully Nonlinear Potential Flow (FNPF-SEM) model developed for the simulation of wave-body interactions between nonlinear free surface waves and impermeable structures. The solver is accelerated using an iterative p-multigrid algorithm. Two cases are considered: (i) a surface piercing box forced into vertical motion cre...

In marine offshore engineering, cost‐efficient simulation of unsteady water waves and their nonlinear interaction with bodies are important to address a broad range of engineering applications at increasing fidelity and scale. We consider a fully nonlinear potential flow (FNPF) model discretized using a Galerkin spectral element method to serve as...

No PDF available ABSTRACT The absorption properties of room surfaces have a major influence on the acoustics of rooms. In wave-based room acoustic simulations it is common practice to model room surfaces using a local-reaction approximation, instead of modeling the full extended-reaction behavior. However, previous research has indicated that the l...

No PDF available ABSTRACT This study presents a new model order reduction technique applied to room acoustic simulations using a high-order numerical scheme based on the spectral element method. The goal is to efficiently simulate iterative design processes in room acoustics, where the room acoustics with different boundary absorption properties ar...

Numerical methods can be used to simulate wave propagation in rooms, with applications in virtual reality and building design. Such methods can be highly accurate but computationally expensive when simulating high frequencies and large domains for long simulation times. Moreover, it is common that solutions are sought for multiple input parameter v...

This paper investigates the optimization of second-order control signals required to produce stable non-linear, deep-water waves using a wedge-shaped, plunger-type wave generator. Both numerical and experimental methods are utilized. A fully non-linear and dispersive potential flow (FNPF) solver developed at DTU is used for the numerical work, foll...

This paper presents ISOPE’s 2020 comparative study on the interaction between focused waves and a fixed cylinder. The paper discusses the qualitative and quantitative comparisons between 20 different numerical solvers from various universities across the world for a fixed cylinder. The moving cylinder cases are reported in a companion paper as part...

Epidemic models are often used without taking into account continuous age-dependent effects, limiting its use to study homogeneous subgroups in a population. An obstacle for using continuous age-dependent epidemic compartment models is the need for efficient numerical solution procedures. In this work, we propose an efficient space and time third-o...

In environmental acoustics and in room acoustics, many surfaces exhibit extended-reaction (ER) behavior, i.e., their surface impedance varies with the angle of the incident sound wave. This paper presents a phenomenological method for modeling such angle dependent surface impedance properties in time-domain wave-based simulations. The proposed meth...

The estimation of extreme loads from waves is an essential part of the design of an offshore wind turbine. Standard design codes suggest to either use simplified methods based on regular waves, or to perform fully nonlinear computations. The former might not provide an accurate representation of the extreme waves, while the latter is computationall...

This paper presents an equivalent fluid model (EFM) formulation in a three-dimensional time-domain discontinuous Galerkin finite element method framework for room acoustic simulations. Using the EFM allows for the modeling of the extended-reaction (ER) behavior of porous sound absorbers. The EFM is formulated in the numerical framework by using the...

We present a massively parallel and scalable nodal Discontinuous Galerkin Finite Element Method (DGFEM) solver for the time-domain linearised acoustic wave equations. The solver is implemented using the libParanumal finite element framework with extensions to handle curvilinear geometries and frequency dependent boundary conditions of relevance in...

In marine offshore engineering, cost-efficient simulation of unsteady water waves and their nonlinear interaction with bodies are important to address a broad range of engineering applications at increasing fidelity and scale. We consider a fully nonlinear potential flow (FNPF) model discretized using a Galerkin spectral element method to serve as...

This paper presents an equivalent fluid model (EFM) formulation in a 3D time-domain dis-continuous Galerkin finite element method framework for room acoustic simulations. Using the EFM allows for the modeling of the extended-reaction (ER) behavior of porous sound absorbers. The EFM is formulated in the numerical framework by using the method of aux...

This abstract presents our progress in the development of a fully nonlinear potential ow solver capable of modelling wave-structure and wave-bottom interactions. The numerical method is based on a finite difference method with a sigma-transform in the vertical direction, as presented in Bingham and Zhang (2007), and boundary conditions are imposed...

Mooring systems exhibit high failure rates. This is especially problematic for offshore renewable energy systems, like wave and floating wind, where the mooring system can be an active component and the redundancy in the design must be kept low. Here we investigate how uncertainty in input parameters propagates through the mooring system and affect...

Nonlinear model predictive control (NMPC) often requires real-time solution to optimization problems. However, in cases where the mathematical model is of high dimension in the solution space, e.g. for solution of partial differential equations (PDEs), black-box optimizers are rarely sufficient to get the required online computational speed. In suc...

We present a new stabilised and efficient high-order nodal spectral element method based on the Mixed Eulerian Lagrangian (MEL) method for general-purpose simulation of fully nonlinear water waves and wave-body interactions. In this MEL formulation a standard Laplace formulation is used to handle arbitrary body shapes using unstructured – possibly...

Extended-reaction modeling in wave-based simulations This paper presents a general method for modeling extended-reaction surface impedance boundary conditions in time-domain wave-based room acoustic simulations. A sound field separation technique is used to separate the sound field at a boundary into its incident and reflected components, in each t...

We apply optimal control to operational optimization to a model of a real oil reservoir, SOLSORT, located in the Danish North Sea. The oil reservoir model is a partial differential equation system that is simulated using a commercial oil reservoir simulator (Eclipse 300). The numerical optimization is conducted using an optimization software tool c...

In environmental acoustics and in room acoustics, many surfaces exhibit extended-reaction (ER) behavior, i.e., their surface impedance varies with the angle of the incident sound wave. This paper presents a phenomenological method for modeling such angle dependent surface impedance properties in time-domain wave-based simulations. The proposed meth...

Many widely used numerical algorithms for option pricing and instrument valuation in finance are computationally expensive. In this work, we explore a means to lower this computational cost by considering a data-driven option pricing approach based on artificial neural networks (ANNs). We consider ANNs for both creating a function approximation of...

POST-CONFERENCE ISOPE 2018 CONTRIBUTION: A 3D fully nonlinear potential flow (FNPF) model based on an Eulerian formulation is presented. The model is discretized using high-order prismatic - possibly curvi-linear - elements using a spectral element method (SEM) that has support for adaptive unstructured meshes. The paper presents details of the FNP...

Results from Blind Test Series 1, part of the Collaborative Computational Project in Wave Structure Interaction (CCP-WSI), are presented. Participants, with a range of numerical methods, simulate blindly the interaction between a fixed structure and focused waves ranging in steepness and direction. Numerical results are compared against correspondi...