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high-order methods; Brinkman penalization; discontinuous Galerkin methods; embedded geometry; high-order boundary; IMEX Runge–Kutta methods; boundary value problems with degeneration of the solution on entire boundary of the domain; the method of finite elements; special graded mesh; multigrid methods; Hermitian/skew-Hermitian splitting method; skew-Hermitian triangular splitting method; strongly non-Hermitian matrix; lie symmetries; invariantized difference scheme; numerical solutions; finite integration method; shifted Chebyshev polynomial; direct and inverse problems; Volterra integro-differential equation; Tikhonov regularization method; quartic spline; triangulation; scattered data; continuity; surface reconstruction; positivity-preserving; interpolation; jaw crusher; symmetrical laser cladding path; FEPG; wear