feat(legacy): add sparse LinearSystem assembly container

Introduce the legacy augmented-system representation used by `Solver`/`Analysis`.

- Track stiffness blocks, constraint matrices, and RHS assembly scratch.

src/legacy/linear_system.jl

@@ -0,0 +1,53 @@
+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/FEMBase.jl/blob/master/LICENSE
+
+mutable struct LinearSystem{Tv, Ti<:Integer}
+    M :: SparseMatrixCSC{Tv, Ti}
+    K :: SparseMatrixCSC{Tv, Ti}
+    Kg :: SparseMatrixCSC{Tv, Ti}
+    C1 :: SparseMatrixCSC{Tv, Ti}
+    C2 :: SparseMatrixCSC{Tv, Ti}
+    D :: SparseMatrixCSC{Tv, Ti}
+    f :: SparseVector{Tv, Ti}
+    fg :: SparseVector{Tv, Ti}
+    g :: SparseVector{Tv, Ti}
+    u :: SparseVector{Tv, Ti}
+    la :: SparseVector{Tv, Ti}
+    dim :: Int
+end 
+
+function LinearSystem(dim::Int)
+    return LinearSystem(spzeros(dim, dim), spzeros(dim, dim),
+                        spzeros(dim, dim), spzeros(dim, dim),
+                        spzeros(dim, dim), spzeros(dim, dim),
+                        spzeros(dim), spzeros(dim), spzeros(dim),
+                        spzeros(dim), spzeros(dim), dim)
+end
+
+abstract type AbstractLinearSystemSolver end
+
+function solve!(::LinearSystem, ::Solver) where Solver<:AbstractLinearSystemSolver
+    @info("This is a placeholder function for solving linear systems. To solve " *
+          "linear systems, you must define a function " *
+          "solve!(system::LinearSystem, solver::$Solver)")
+end
+
+function can_solve(::LinearSystem, ::Solver) where Solver<:AbstractLinearSystemSolver
+    return (true, "OK")
+end
+
+function solve!(ls::LinearSystem, solvers::Vector{S}) where S<:AbstractLinearSystemSolver
+    for solver in solvers
+        Solver = typeof(solver)
+        cansolve, msg = can_solve(ls, solver)
+        if !cansolve
+            @info("Solver $Solver cannot solve linear system: $msg")
+            continue
+        end
+        timeit("solve linear system using solver $Solver") do
+            solve!(ls, solver)
+        end
+        return
+    end
+    error("Failed to solve linear system.")
+end