Aim of the Journal

Engineering analysis with boundary elements is dedicated to the latest developments of engineering analysis with boundary elements, mesh reduction, and other related innovative and emerging numerical methods. The journal founded in 1984 was originally focused on the development of the Boundary Element Method. Its scope has since been expanded to include the emerging mesh reduction and meshless methods. The aim of the journal is to promote the use of non-traditional, innovative, and emerging computational methods for the analyses of modern engineering problems.

Scope

Engineering Analysis with Boundary Elements publishes topics including:
• Boundary Element Methods
• Method of Fundamental Solutions and Related Methods
• Radial Basis Function Collocation Methods
• Other Mesh Reduction and Meshless Methods
• Particle Methods
• Other Emerging and Non-Traditional Numerical Methods
• Advanced Engineering Analyses and Applications

Special Issue on Modern Kernel Methods and Applications: In Honor of Robert Schaback’s 80th Birthday
Día de Entrega: 2026-03-31

This Special Issue features recent advances in modern kernel methods and their applications in approximation theory, meshless techniques, and PDE solution methods, inspired by the foundational contributions of Robert Schaback. Selected works originate from the 2026 Hong Kong meeting honoring his 80th birthday, complemented by an open call to the wider community. Topics include radial basis functions, kernel-based approximation, stability and error analysis, scalable solvers, and real-world engineering applications aligned with Engineering Analysis with Boundary Elements.

Guest editors:

Prof. Leevan Ling
Hong Kong Baptist University
lling@hkbu.edu.hk 

Prof. Stefano De Marchi
Università degli Studi di Padova
stefano.demarchi@unipd.it

Prof. Christian Rieger
Philipps-Universität Marburg
riegerc@mathematik.uni-marburg.de 

Prof. Emma Perracchione
Politecnico di Torino
emma.perracchione@polito.it 

Prof. Robert Schaback
University of Göttingen
schaback@math.uni-goettingen.de 

Special issue information:

This Special Issue showcases recent advances in modern kernel-based methods and their applications in approximation theory, meshless techniques, and partial differential equation (PDE) solution methods, inspired by the foundational contributions of Robert Schaback to the field. Selected high-quality works originate from the Conference on Modern Kernel Methods and Applications held in Hong Kong in 2026, celebrating Professor Schaback's 80th birthday, and are complemented by submissions from an open call to the broader international research community.

The scope encompasses both theoretical developments and practical applications of kernel and radial basis function (RBF) methods, with particular emphasis on topics aligned with Engineering Analysis with Boundary Elements. Contributions may address:

Theoretical Foundations:
• Approximation theory for kernel-based interpolation and scattered data approximation
• Stability analysis, conditioning, and error estimates for RBF methods
• Convergence theory and native space frameworks
• Positive definiteness and reproducing kernel Hilbert spaces (RKHS)
• Multivariate interpolation and approximation in high dimensions

Numerical Methods and Algorithms:
• Meshless and mesh-free discretization techniques for PDEs
• RBF collocation methods (Kansa method, Hermite collocation, etc.)
• Method of fundamental solutions (MFS) and method of particular solutions
• Strong-form and weak-form collocation approaches
• Fast algorithms and computational efficiency improvements for large-scale problems
• Scalable solvers and preconditioning strategies
• Adaptive refinement and greedy algorithms

Advanced Techniques:
• Kernel methods for complex geometries, irregular domains, and moving boundaries
• Surface and manifold approximation using kernel methods
• Nonlocal operators and fractional PDE modeling
• Data-driven kernel selection and machine learning-enhanced approaches
• Hybrid methods combining kernels with finite elements, finite differences, or neural networks
• Multi-scale and multi-resolution kernel techniques

Engineering and Scientific Applications:
• Boundary element methods (BEM) enhanced by kernel techniques
• Computational fluid dynamics and aerodynamics
• Structural mechanics, elasticity, and solid mechanics problems
• Heat transfer, diffusion, and transport phenomena
• Acoustics and wave propagation
• Electromagnetic field computations
• Geophysics and environmental engineering applications
• Biomedical engineering and computational biology
• Real-world industrial and interdisciplinary applications

Papers should present original research with rigorous mathematical analysis, robust numerical validation, and/or significant application impact. Review articles on emerging directions in kernel methods are also welcome.