In this article, we present Bembel, the C++ library featuring higher order isogeometric Galerkin boundary element methods for Laplace, Helmholtz, and Maxwell problems. Bembel is compatible with geometries from Octave NURBS package, provides an interface to Eigen template linear algebra operations. For computational efficiency, it applies embedded fast multipole method tailored analysis framework a parallel matrix assembly based on OpenMP.

Abstract We solve acoustic scattering problems by means of the isogeometric boundary integral equation method. In order to avoid spurious modes, we apply combined field equations for either sound-hard scatterers or sound-soft scatterers. These are discretized Galerkin’s method, which especially enables mathematically correct regularization hypersingular operator. circumvent densely populated system matrices, employ embedded fast multipole is based on interpolation kernel function under...

Electroplating of dysprosium from several nonaqueous solutions and an ionic liquid was studied. Dysprosium metal used as the anode material, metals a silicon wafer with vacuum-deposited gold layer were cathode materials. successfully electroplated dimethylformamide-based high coulombic efficiency. The resulting effectively protected vs reactions water oxygen air by electroplating aluminum onto electrolyte. All processes investigated electrochemical methods including cyclic voltammetry,...

The hydrolysis of lithium bis[1,2-oxalato(2-)-O,O′] borate (LiBOB) was investigated in pure water and solutions acetonitrile at low content. reaction can easily be observed by time-dependent conductivity measurements as protons are generated the first step hydrolysis. results these evaluated according to a pseudo order. Hydrolysis other borates also studied for comparison. In solvent, is much more complicated. NMR studies show very slow LiBOB with resulting equilibria, depending on content...

We develop a new framework for embedding (joint) probability distributions in tensor product reproducing kernel Hilbert spaces (RKHS). This accommodates low-dimensional, positive, and normalized model of Radon-Nikodym derivative, estimated from sample sizes up to several million data points, alleviating the inherent limitations RKHS modeling. Well-defined positive conditional are natural by-products our approach. The is fast compute naturally learning problems ranging prediction...

Abstract We propose a sparse algebra for samplet compressed kernel matrices to enable efficient scattered data analysis. show that the compression of by means samplets produces optimally in certain S -format. The can be performed cost and memory scale essentially linearly with number points kernels finite differentiability. same holds true addition multiplication -formatted matrices. prove inverse matrix, given it exists, is compressible -format as well. use selected inversion allows...

This paper describes a fast multichannel precision thermometer working in temperature range from -50degC to +40degC. Thermistors are used as sensing elements. A detailed discussion of the choice thermistor and design circuitry is given. It shown that accuracy similar calibrated platinum thermometers can be achieved by calibration thermistors. During our tests, was both mathematically experimentally analyzed detail. The stability 30 thermistors after six months laboratory use analyzed....

We introduce the concept of samplets by transferring construction Tausch-White wavelets to scattered data. This way, we obtain a multiresolution analysis tailored discrete data which directly enables compression, feature detection and adaptivity. The cost for constructing samplet basis fast transform, respectively, is O(N), where N number points. Samplets with vanishing moments can be used compress kernel matrices, arising, instance, in based learning approximation. result are sparse...

The Karl Fischer titration is the standard method for determination of water content in many materials. However, particular cases, unwanted side reactions occur which leads to unacceptably large errors. We present here an nuclear magnetron resonance (NMR)-based trace impurities a salt recently developed lithium ion cells, i.e., bis[1,2-oxalato(2-)-O,O']borate (LiBOB). method, may be applied salts used batteries, able determine traces down ∼6 ppm. Errors depend strongly on studied. Deviations...

We have shown that conductivity optima of battery electrolytes can be determined with the help measurements guided by a program based on simplex algorithm. The method was successfully checked us data from literature. In addition, series at −25°C for lithium bis[1,2-oxalato(2-)-]borate (LiBOB) in various solvent blends performed, where suggestions this composition and salt concentration were applied. Data 25 several LiBOB ethylene carbonate (EC)/propylene (PC)/dimethyl (DMC), EC/PC/DMC/ethyl...

In this article, we consider fast direct solvers for nonlocal operators. The pivotal idea is to combine a wavelet representation of the system matrix, yielding quasi-sparse with nested dissection ordering scheme. latter drastically reduces fill-in during factorization matrix by means Cholesky decomposition or an LU decomposition, respectively. This way, end up exact inverse compressed only moderate increase number nonzero entries in matrix. To illustrate efficacy approach, conduct numerical...

In electrocardiography, the "classic" inverse problem is reconstruction of electric potentials at a surface enclosing heart from remote recordings body and an accurate description anatomy. The latter being affected by noise obtained with limited resolution due to clinical constraints, possibly large uncertainty may be perpetuated in reconstruction. purpose this work study effect shape on forward electrocardiography. To aim, first recast into boundary integral formulation then discretised...

We investigated 13 additives well known from literature and studied their effect on the performance of lithiumion cells comprised electrolytes based lithium bis[1,2-oxalato(2-)-OO´] borate. The can be attributed to three classes including chemically modified solvents, metal salts, oligoethers. In contrast similar studies in literature, where often only a single additive was investigated, under same conditions at cycled up 500 times 60°C thermostat. internal resistance charge capacity are...

The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context hierarchical matrices, this can be realized by structured blockwise low-rank resulting almost linear cost. However, efficiency algorithm based on a recursive scheme which makes error analysis quite involved. article, we propose new algorithmic framework for matrices. It improves currently known implementations reducing to suitable approximations sums matrix products. We several...

Multilevel quadrature methods for parametric operator equations such as the multilevel (quasi--) Monte Carlo method resemble a sparse tensor product approximation between spatial variable and parameter. We employ this fact to reverse by applying differences of rules finite element discretizations increasing resolution. Besides being algorithmically more efficient if underlying are nested, way performing enables easy use nonnested even adaptively refined meshes. moreover provide rigorous...