On the numerical solution of minimal energy problems

DOI10.1080/17476930903394986zbMath1206.31008OpenAlexW2125575828MaRDI QIDQ3061262

Günther Of, Wolfgang L. Wendland, Natalia Zorii

Publication date: 14 December 2010

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: http://openlib.tugraz.at/590c16f313b65

zbMATH Keywords

boundary element approximationsimple layer boundary integral operatorLipschitz surfacedual condenser problemminimal Newtonian energy problempenalty me-thod

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Existence of solutions for minimax problems (49J35) Discrete potential theory (31C20) Potentials and capacities on other spaces (31C15) Linear integral equations (45A05)

Related Items (14)

Constrained energy problems with external fields for vector measures ⋮ Rapid Solution of Minimal Riesz Energy Problems ⋮ Constrained minimum Riesz energy problems for a condenser with intersecting plates ⋮ Equilibrium problems for infinite dimensional vector potentials with external fields ⋮ Minimal energy problems for strongly singular Riesz kernels ⋮ On Riesz minimal energy problems ⋮ A concept of weak Riesz energy with application to condensers with touching plates ⋮ Riesz minimal energy problems on Ck−1,1-manifolds ⋮ Various concepts of Riesz energy of measures and application to condensers with touching plates ⋮ Condensers with touching plates and constrained minimum Riesz and Green energy problems ⋮ Necessary and sufficient conditions for the solvability of the Gauss variational problem for infinite dimensional vector measures ⋮ Condensers with infinitely many touching Borel plates and minimum energy problems ⋮ An alternative concept of Riesz energy of measures with application to generalized condensers ⋮ Distributing many points on spheres: minimal energy and designs

Cites Work

• The integral equation method and the Neumann problem for the Poisson equation on NTA domains
• Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
• Some Historical Remarks on the Positivity of Boundary Integral Operators
• Artificial Multilevel Boundary Element Preconditioners
• Numerical Approximation Methods for Elliptic Boundary Value Problems
• Extremal problems dual to the Gauss variational problem
• Boundary Integral Operators on Lipschitz Domains: Elementary Results
• The fast multipole method for the symmetric boundary integral formulation
• On C. Neumann's method for second-order elliptic systems in domains with non-smooth boundaries

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