Related papers: Variational formulation and monolithic solution of…
An inverse-free dynamical system is proposed to solve the generalized absolute value equation (GAVE) with a fixed time convergence, where the time of convergence is finite and is uniformly bounded for all initial points. Moreover, an…
We advocate a domain specific software development methodology for heterogeneous computing platforms such as Multicore CPUs, GPUs and FPGAs. We argue that three specific benefits are realised from adopting such an approach: portable,…
To investigate solutions of (near-)optimal control problems, we extend and exploit a notion of homogeneity recently proposed in the literature for discrete-time systems. Assuming the plant dynamics is homogeneous, we first derive a scaling…
This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…
In this paper, we address a way to reduce the total computational cost of meshless approximation by reducing the required stencil size through spatial variation of computational node regularity. Rather than covering the entire domain with…
Isogeometric analysis (IGA) represents a recently developed technology in computational mechanics that offers the possibility of integrating methods for analysis and Computer Aided Design (CAD) into a single, unified process. The…
The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
In differential equation discovery algorithms, numerical differentiation is usually a fixed preliminary step. Current methods improve robustness with data subsampling and sparsity but often ignore the variability from the differentiation…
This paper is concerned with the analysis of a new stable space-time finite element method (FEM) for the numerical solution of parabolic evolution problems in moving spatial computational domains. The discrete bilinear form is elliptic on…
Incremental determinization is a recently proposed algorithm for solving quantified Boolean formulas with one quantifier alternation. In this paper, we formalize incremental determinization as a set of inference rules to help understand the…
Numerical homogenization tries to approximate the solutions of elliptic partial differential equations with strongly oscillating coefficients by functions from modified finite element spaces. We present in this paper a class of such methods…
We propose quantum methods for solving differential equations that are based on a gradual improvement of the solution via an iterative process, and are targeted at applications in fluid dynamics. First, we implement the Jacobi iteration on…
The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…
We present a novel approach that redefines the traditional interpretation of explicit and implicit discretization methods for solving a general class of advection-diffusion equations (ADEs) featuring nonlinear advection, diffusion…
Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially…
We present a novel space-time isogeometric discretization of the acoustic wave equation in second-order formulation that is intrinsically unconditionally stable. The method relies on a variational framework inspired by [Walkington 2014],…
We introduce a generalized finite difference method for solving a large range of fully nonlinear elliptic partial differential equations in three dimensions. Methods are based on Cartesian grids, augmented by additional points carefully…
We present a simple and efficient variational finite difference method for simulating time-dependent Stokes flow in the presence of irregular free surfaces and moving solid boundaries. The method uses an embedded boundary approach on…
We present a new fixed mesh algorithm for solving a class of interface inverse problems for the typical elliptic interface problems. These interface inverse problems are formulated as shape optimization prob- lems whose objective…