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Self-consistent field theory (SCFT) has proven to be a powerful tool for modeling equilibrium microstructures of soft materials, particularly for multiblock polymers. A very successful approach to numerically solving the SCFT set of…
In this work, we present a study combining two approaches in the context of solving PDEs: the continuous finite element method (FEM) and more recent techniques based on neural networks. In recent years, physics-informed neural networks…
This work presents a study on the computational homogenization of electro-magneto-mechanically coupled problems through the Virtual Element Method (VEM). VE-approaches have great potential for the homogenization of the physical properties…
In this paper we address three aspects of nonlinear computational homogenization of elastic solids by two-scale finite element methods. First, we present a nonlinear formulation of the finite element heterogeneous multiscale method FE-HMM…
The Fredholm-Hammerstein integral equations (FHIEs) with weakly singular kernels exhibit multi-point singularity at the endpoints or boundaries. The dense discretized matrices result in high computational complexity when employing numerical…
In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by affine decomposition of the geometry or by the design element…
Conventional classical solvers are commonly used for solving matrix equation systems resulting from the discretization of SIEs in computational electromagnetics (CEM). However, the memory requirement would become a bottleneck for classical…
The development of personalized human head models from medical images has become an important topic in the electromagnetic dosimetry field, including the optimization of electrostimulation, safety assessments, etc. Human head models are…
Partial differential equations (PDEs) underlie our understanding and prediction of natural phenomena across numerous fields, including physics, engineering, and finance. However, solving parametric PDEs is a complex task that necessitates…
For an accurate description of electromagneto-thermomechanical systems, electromagnetic fields need to be described in a Eulerian frame, whereby the thermomechanics is solved in a Lagrangean frame. It is possible to map the Eulerian frame…
This paper presents new fast algorithms for Hermite interpolation and evaluation over finite fields of characteristic two. The algorithms reduce the Hermite problems to instances of the standard multipoint interpolation and evaluation…
This work presents the Griffith-type phase-field formation at large deformation in the framework of adaptive edge-based smoothed finite element method (ES-FEM) for the first time. Therein the phase-field modeling of fractures has attracted…
The finite element method (FEM) is a cornerstone numerical technique for solving partial differential equations (PDEs). Here, we present $\textbf{Qu-FEM}$, a fault-tolerant era quantum algorithm for the finite element method. In contrast to…
The Finite element method (FEM) has long served as the computational backbone for topology optimization (TO). However, for designing structures undergoing large deformations, conventional FEM-based TO often exhibits numerical instabilities…
Extensive research papers of three-dimensional computational techniques are widely used for the investigation of human brain pathophysiology. Eddy current analyzing could provide an indication of conductivity change within a biological…
Achieving accurate numerical results of hydrodynamic loads based on the potential-flow theory is very challenging for structures with sharp edges, due to the singular behavior of the local-flow velocities. In this paper, we introduce the…
We develop a sparse hierarchical $hp$-finite element method ($hp$-FEM) for the Helmholtz equation with variable coefficients posed on a two-dimensional disk or annulus. The mesh is an inner disk cell (omitted if on an annulus domain) and…
A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…