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Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs is about the interplay between modeling, analysis, discretization, matrix computation, and model reduction. The authors link PDE analysis, functional analysis, and calculus of variations with matrix iterative computation using Krylov subspace methods and address the challenges that arise during formulation of the mathematical model through to efficient numerical solution of the algebraic problem. The book's central concept, preconditioning of the conjugate gradient method, is traditionally developed algebraically using the preconditioned finite-dimensional algebraic system. In this text, however, preconditioning is connected to the PDE analysis, and the infinite-dimensional formulation of the conjugate gradient method and its discretization and preconditioning are linked together. This text challenges commonly held views, addresses widespread misunderstandings, and formulates thought-provoking open questions for further research.
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Numerical solutions of differential equations --- Integral equations --- Equations intégrales --- Numerical solutions --- Solutions numériques --- 519.61 --- -Equations, Integral --- Functional equations --- Functional analysis --- Numerical methods of algebra --- Numerical solution --- Numerical solutions. --- -Numerical methods of algebra --- Numerical solution. --- 519.61 Numerical methods of algebra --- -519.61 Numerical methods of algebra --- Equations, Integral --- Equations intégrales --- Solutions numériques --- Numerical analysis --- Analyse numérique. --- Analyse numérique --- Numerical analysis. --- Integral equations - Numerical solutions --- Equations integrales --- Methodes numeriques
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Numerical analysis --- Analyse numérique --- Congresses --- Congrès --- -#KVIV --- 519.6 --- 681.3*G1 --- Mathematical analysis --- Computational mathematics. Numerical analysis. Computer programming --- Congresses. --- 681.3*G1 Numerical analysis --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- #KVIV --- NUMERICAL SOLUTION --- MATHEMATICS --- Monograph --- Mathematics. --- Math --- Science --- Analyse numérique. --- Numerical analysis - Congresses --- Analyse numérique.
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Equations --- Algebra --- Numerical solutions --- Data processing. --- Linear equations --- Systems --- Numerical solution --- Computation by computer systems --- Computation by computer systems. --- Analyse numérique. --- Algèbre linéaire. --- Numerical analysis --- Algebras, Linear --- Itération (mathématiques) --- Iterative methods (Mathematics) --- Analyse numérique --- Algèbre linéaire --- Numerical analysis. --- Algebras, Linear. --- Itération (mathématiques) --- Programmation mathematique --- Programmation lineaire
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Differential equations, Partial --- Equations aux dérivées partielles --- Numerical solutions --- Solutions numériques --- -Partial differential equations --- -Numerical solutions --- Numerical solutions of differential equations --- Partial differential equations --- Numerical solutions. --- Numerical analysis --- NUMERICAL SOLUTION --- DIFFERENTIAL EQUATIONS --- Monograph --- Differential equations. --- Equations, Differential --- Bessel functions --- Calculus
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Numerical analysis --- Équations différentielles --- Solution numérique --- --4191 --- 519.6 --- 681.3 *G18 --- 681.3*G17 --- 10.04 --- Computational mathematics. Numerical analysis. Computer programming --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- Verzekeringswiskunde ; Numerieke analyse --- Differential equations --- Numerical solutions. --- Numerical solution --- Numerical solution. --- 681.3*G17 Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Équations aux dérivées partielles. --- Differential equations, Partial. --- Analyse numérique. --- Équation différentielle --- --Solution numérique --- --Analyse numérique. --- --519.6 --- Analyse numérique. --- Équations aux dérivées partielles.
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Differential equations, Partial --- Iterative methods (Mathematics) --- Sparse matrices --- Equations aux dérivées partielles --- Itération (Mathématiques) --- Matrices éparses --- Numerical solutions --- Solutions numériques --- Sparse matrices. --- Numerical solutions. --- -Iterative methods (Mathematics) --- 519.61 --- 681.3*G13 --- Spare matrix techniques --- Matrices --- Iteration (Mathematics) --- Numerical analysis --- Partial differential equations --- Numerical methods of algebra --- Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 681.3*G13 Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 519.61 Numerical methods of algebra --- Equations aux dérivées partielles --- Itération (Mathématiques) --- Matrices éparses --- Solutions numériques --- Iterative methods (Mathematics). --- Differential equations, Partial - Numerical solutions. --- Differential equations, Partial-Numerical solution
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Since their discovery, multi-walled carbon nanotubes (MWCNTs) have received tremendous attention due to their unique electrical, optical, physical, chemical, and mechanical properties. Remarkable advances have been made in the synthesis, purification, structural characterization, functionalization, and application of MWCNTs. Their particular characteristics make them well suited for a plethora of applications in a number of fields, namely nanoelectronics, nanofluids, energy management, (electro)catalysis, materials science, construction of (bio)sensors based on different detection schemes, multifunctional nanoprobes for biomedical imaging, and sorbents for sample preparation or removal of contaminants from wastewater. They are also useful as anti-bacterial agents, drug delivery nanocarriers, etc. The current relevant application areas are countless. This Special Issue presents original research and review articles that address advances, trends, challenges, and future perspectives regarding synthetic routes, structural features, properties, behaviors, and industrial or scientific applications of MWCNTs in established and emerging areas.
graphene oxide --- n/a --- Multi-Walled Carbon Nanotube (MWCNT) --- elution --- gold nanoparticles --- MHD --- heck reaction --- drug delivery --- carbon-nanotubes --- water based nanofluid --- zeolitic imidazolate framework --- Ionic liquid --- electroanalysis --- curved stretching sheet --- multiwalled carbon nanotubes --- lubricating oil additives --- hydrophobic drugs --- agricultural irrigation water --- polarity --- cerium oxide --- adsorption --- electrical properties --- non-linear thermal radiation --- electrochemical properties --- nanomaterials --- radar absorbing materials --- chloride diffusion --- RAFT polymerization --- synthesis methods --- gold(III) --- mechanical properties --- dissolution rate --- carbon materials --- electrochemical sensors --- magnetic solid phase extraction --- silicone rubber --- Single-Walled Carbon Nanotube (SWCNT) --- Pd-CNT nanohybrids --- kinetics --- nonylphenol --- boundary layer --- Casson model --- sensing applications --- organochlorine pesticides --- composites --- multi-wall carbon nanotube (MWCNT) --- polymeric composites --- carbon nanotubes --- structural --- azide-alkyne click chemistry --- functionalized carbon nanotubes --- heat generation --- EMI shielding --- gold(I) --- cement mortars --- semi-homogeneous catalysis --- functionalized CNTs --- nanomedicine --- multi-walled carbon nanotubes --- numerical solution --- PMMA --- HAM --- complex permittivity --- thermal radiation --- stretching sheet
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