Related papers: Neglecting discretization corrections in regulariz…
Overdetermined systems of first kind integral equations appear in many applications. When the right-hand side is discretized, the resulting finite-data problem is ill-posed and admits infinitely many solutions. We propose a numerical method…
We propose a new a posteriori error estimator for mixed finite element discretizations of the curl-curl problem. This estimator relies on a Prager--Synge inequality, and therefore leads to fully guaranteed constant-free upper bounds on the…
The notions of discrete conformality on triangle meshes have rich mathematical theories and wide applications. The related notions of discrete uniformizations on triangle meshes, suggest efficient methods for computing the uniformizations…
A simple theory for the leading-order correction g_1(r) to the structure of a hard-sphere liquid with discrete (e.g. square-well) potential perturbations is proposed. The theory makes use of a general approximation that effectively…
Motivated by recent applications in rough volatility and regularity structures, notably the notion of singular modelled distribution, we study paths, rough paths and related objects with a quantified singularity at zero. In a pure path…
Singularity swap quadrature (SSQ) is an effective method for the evaluation at nearby targets of potentials due to densities on curves in three dimensions. While highly accurate in most settings, it is known to suffer from catastrophic…
Identification of model parameters in computer simulations is an important topic in computer experiments. We propose a new method, called the projected kernel calibration method, to estimate these model parameters. The proposed method is…
This work proposes four novel hybrid quadrature schemes for the efficient and accurate evaluation of weakly singular boundary integrals (1/r kernel) on arbitrary smooth surfaces. Such integrals appear in boundary element analysis for…
In this paper, we develop a new deflation technique for refining or verifying the isolated singular zeros of polynomial systems. Starting from a polynomial system with an isolated singular zero, by computing the derivatives of the input…
Kernel density estimators with circular data have been studied extensively for decades, as they allow flexible estimations even when the shape of the underlying density is complex. Many recent studies have examined bias correction methods;…
Field measurements for direct current (DC) resistivity imaging, used for subsurface profiling, are frequently conducted over undulating terrain. Accurately incorporating such topographic variations in its forward modelling is essential for…
This paper is concerned with approximations and related discretization error estimates for the normal derivatives of solutions of linear elliptic partial differential equations. In order to illustrate the ideas, we consider the Poisson…
This paper shows how numerical methods on a regular grid in a box can be used to generate numerical schemes for problems in general smooth domains contained in the box with no need for a domain specific discretization. The focus is mainly…
Linear approximation approaches suffer from Gibbs oscillations when approximating functions with singularities. ENO-SR resolution is a local approach avoiding oscillations and with a full order of accuracy, but a loss of regularity of the…
In this paper, we will present advanced discretization methods for solving retarded potential integral equations. We employ a $C^{\infty}$-partition of unity method in time and a conventional boundary element method for the spatial…
Integral equation methods for the solution of partial differential equations, when coupled with suitable fast algorithms, yield geometrically flexible, asymptotically optimal and well-conditioned schemes in either interior or exterior…
We introduce a geometric realization of noncommutative singularity resolutions. To do this, we first present a new conjectural method of obtaining conventional resolutions using coordinate rings of matrix-valued functions. We verify this…
We consider a polynomial reconstruction of smooth functions from their noisy values at discrete nodes on the unit sphere by a variant of the regularized least-squares method of An et al., SIAM J. Numer. Anal. 50 (2012), 1513--1534. As nodes…
With the help of hyper-ideal circle pattern theory, we have developed a discrete version of the classical uniformization theorems for surfaces represented as finite branched covers over the Riemann sphere as well as compact polyhedral…
In this paper, we study the singularities of Feynman integrals using homological techniques. We analyse the Feynman integrals by compactifying the integration domain as well as the ambient space by embedding them in higher-dimensional…