### Recent Submissions

• #### Gaussian quadrature for $C^1$ cubic Clough-Tocher macro-triangles ﻿

(Journal of Computational and Applied Mathematics, 2018-10-31)
A numerical integration rule for multivariate cubic polynomials over n-dimensional simplices was designed by Hammer and Stroud [14]. The quadrature rule requires n + 2 quadrature points: the barycentre of the simplex and ...
• #### Generalization of the Pythagorean Eigenvalue Error Theorem and its Application to Isogeometric Analysis ﻿

(Numerical Methods for PDEs, 2018-10-13)
This chapter studies the effect of the quadrature on the isogeometric analysis of the wave propagation and structural vibration problems. The dispersion error of the isogeometric elements is minimized by optimally blending ...
• #### International energy agency ocean energy systems task 10 wave energy converter modeling verification and validation ﻿

(Proceedings of European Wave and Tidal Energy Conference, 2017)
This is the first joint reference paper for the Ocean Energy Systems (OES) Task 10 Wave Energy Converter modeling verification and validation group. The group is established under the OES Energy Technology Network program ...
• #### A partition of unity finite element method for computational diffusion MRI ﻿

(Journal of Computational Physics, 2018)
The Bloch–Torrey equation describes the evolution of the spin (usually water proton) magnetization under the influence of applied magnetic field gradients and is commonly used in numerical simulations for diffusion MRI ...
• #### Simulation of the HarshLab floating platform for offshore experimentation using FEniCS-HPC ﻿

(Poster EUSKAMPUS IV Marine Energy Conference, 2017)
• #### Direct finite element simulation of turbulent flow for marine based renewable energy ﻿

(Companion paper to F. Wendt, et. al. International energy agency ocean energy systems task 10 wave energy converter modeling verification and validation. In 12th European Wave and Tidal Energy Conference, 2017., 2017)
In this article we present a computational framework for simulation of turbulent flow in marine based renewable energy applications. In particular, we focus on floating structures and rotating turbines. This work is an ...
• #### A Numerical 1.5D Method for the Rapid Simulation of Geophysical Resistivity Measurements ﻿

(Geosciences, 2018-06-14)
In some geological formations, borehole resistivity measurements can be simulated using a sequence of 1D models. By considering a 1D layered media, we can reduce the dimensionality of the problem from 3D to 1.5D via a ...
• #### Numerical simulation of the von Kármán sodium dynamo experiment ﻿

(Journal of Fluid Mechanics, 2018-09-03)
We present hydrodynamic and magnetohydrodynamic (MHD) simulations of liquid sodium flows in the von Kármán sodium (VKS) set-up. The counter-rotating impellers made of soft iron that were used in the successful 2006 experiment ...
• #### Goal-oriented adaptivity using unconventional error representations for the multi-dimensional Helmholtz equation ﻿

(International Journal for Numerical Methods in Engineering, 2017-06-27)
In goal‐oriented adaptivity, the error in the quantity of interest is represented using the error functions of the direct and adjoint problems. This error representation is subsequently bounded above by element‐wise error ...
• #### Refined Isogeometric Analysis for a Preconditioned Conjugate Gradient Solver ﻿

(Computer Methods in Applied Mechanics and Engineering, 2018-06-15)
Starting from a highly continuous Isogeometric Analysis (IGA) discretization, refined Isogeometric Analysis (rIGA) introduces $C^0$ hyperplanes that act as separators for the direct LU factorization solver. As a result, ...
• #### On numerical quadrature for $C^1$ quadratic Powell-Sabin 6-split macro-triangles ﻿

(Journal of Computational and Applied Mathematics, 2018-08-01)
The quadrature rule of Hammer and Stroud [16] for cubic polynomials has been shown to be exact for a larger space of functions, namely the $C^1$ cubic Clough-Tocher spline space over a macro-triangle if and only if the ...
• #### Variational multiscale stabilization for compressible flow ﻿

(Computer Methods in Applied Mechanics and Engineering, 2018)
This paper presents a variational multiscale stabilization for the finite element numerical solution of the Euler and Navier-Stokes equations of compressible flow. All the components of the dual operator are considered in ...
• #### On intermediate-scale open-sea experiments on floating offshore structures: Feasibility and application on a spar support for offshore wind turbines ﻿

(Marine Structures, 2018-06-28)
Experimental investigation of floating structures represents the most direct way for achieving their dynamic identification and it is particularly valuable for relatively new concepts, such as floating supports for offshore ...
• #### REFINED ISOGEOMETRIC ANALYSIS: A SOLVER-BASED DISCRETIZATION METHOD ﻿

(2018-06-22)
Isogeometric analysis (IGA) is a computational approach frequently employed nowadays to study problems governed by partial differential equations (PDEs). This approach defines the geometry using conventional computer-aided ...
• #### Efficient quadrature rules for subdivision surfaces in isogeometric analysis ﻿

(Computer Methods in Applied Mechanics and Engineering, 2018-10)
We introduce a new approach to numerical quadrature on geometries defined by subdivision surfaces based on quad meshes in the context of isogeometric analysis. Starting with a sparse control mesh, the subdivision process ...
• #### Fast 2.5D Finite Element Simulations of Borehole Resistivity Measurements ﻿

(Computational Geosciences, 2018-05-29)
We develop a rapid 2.5-dimensional (2.5D) finite element method for simulation of borehole resistivity measurements in transversely isotropic (TI) media. The method combines arbitrary high-order $H^1$ - and $H$ (curl)-conforming ...
• #### A $C^0$ INTERIOR PENALTY DISCONTINUOUS GALERKIN METHOD FOR FOURTH ORDER TOTAL VARIATION FLOW ﻿

(Journal of Mathematical analysis and applications, 2017)
We consider the numerical solution of a fourth order total variation flow problem representing surface relaxation below the roughening temperature. Based on a regularization and scaling of the nonlinear fourth order parabolic ...
• #### Finite Element Simulations of Logging-While-Drilling and Extra-Deep Azimuthal Resistivity Measurements using Non-Fitting Grids ﻿

(Computational Geosciences, 2018-04-27)
We propose a discretization technique using non-fitting grids to simulate magnetic field-based resistivity logging measurements. Non-fitting grids are convenient because they are simpler to generate and handle than fitting ...
• #### Highly-accurate 5-axis flank CNC machining with conical tools ﻿

(The International Journal of Advanced Manufacturing Technology, 2018-04)
A new method for $5$-axis flank computer numerically controlled (CNC) machining using a predefined set of tappered ball-end-mill tools (aka conical) cutters is proposed. The space of lines that admit tangential motion of ...
• #### On Adomian Based Numerical Schemes for Euler and Navier-Stokes Equations, and Application to Aeroacoustic Propagation ﻿

(2018-03-12)
In this thesis, an Adomian Based Scheme (ABS) for the compressible Navier-Stokes equations is constructed, resulting in a new multiderivative type scheme not found in the context of fluid dynamics. Moreover, this scheme ...